LMFDB - Embedded newform 135.2.p.a.124.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(4,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.13
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.13

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06000 - 1.26326i) q^{2} +(-0.958575 - 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-0.908813 - 2.04305i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(-1.22191 - 0.215456i) q^{7} +(1.82882 + 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +(-3.54425 - 1.01757i) q^{10} +(3.30366 - 1.20243i) q^{11} +(-0.902344 + 0.859377i) q^{12} +(0.380059 + 0.452936i) q^{13} +(-1.56741 + 1.31521i) q^{14} +(-2.07617 + 3.26948i) q^{15} +(4.62449 - 1.68318i) q^{16} +(4.46967 - 2.58056i) q^{17} +(2.26180 + 4.39990i) q^{18} +(-1.41748 + 2.45515i) q^{19} +(-1.33397 + 0.899132i) q^{20} +(0.860474 + 1.96928i) q^{21} +(1.98290 - 5.44797i) q^{22} +(-6.59324 + 1.16257i) q^{23} +(-0.229849 - 3.65042i) q^{24} +(-3.34812 + 3.71350i) q^{25} +0.975040 q^{26} +(5.10397 - 0.974431i) q^{27} +0.892646i q^{28} +(7.21421 + 6.05345i) q^{29} +(1.92947 + 6.08840i) q^{30} +(0.196771 + 1.11595i) q^{31} +(1.33116 - 3.65733i) q^{32} +(-4.90146 - 3.61329i) q^{33} +(1.47793 - 8.38176i) q^{34} +(0.670302 + 2.69224i) q^{35} +(2.10471 + 0.477957i) q^{36} +(-4.06570 + 2.34734i) q^{37} +(1.59896 + 4.39311i) q^{38} +(0.289098 - 0.982452i) q^{39} +(0.495142 - 4.69597i) q^{40} +(4.43129 - 3.71830i) q^{41} +(3.39982 + 1.00044i) q^{42} +(-0.739520 - 2.03181i) q^{43} +(-1.26465 - 2.19044i) q^{44} +(6.70677 - 0.138934i) q^{45} +(-5.52022 + 9.56131i) q^{46} +(-6.14268 - 1.08312i) q^{47} +(-6.86110 - 5.05791i) q^{48} +(-5.13120 - 1.86760i) q^{49} +(1.14211 + 8.16587i) q^{50} +(-8.00727 - 3.97434i) q^{51} +(0.273427 - 0.325858i) q^{52} +8.21098i q^{53} +(4.17926 - 7.48054i) q^{54} +(-5.45905 - 5.65676i) q^{55} +(-2.00717 - 1.68421i) q^{56} +(4.90059 - 0.308566i) q^{57} +(15.2942 - 2.69677i) q^{58} +(-12.6981 - 4.62173i) q^{59} +(2.57581 + 1.06252i) q^{60} +(-1.38440 + 7.85133i) q^{61} +(1.61831 + 0.934331i) q^{62} +(2.01608 - 3.12903i) q^{63} +(1.71215 + 2.96553i) q^{64} +(0.579970 - 1.18811i) q^{65} +(-9.76008 + 2.36173i) q^{66} +(2.83000 + 3.37266i) q^{67} +(-2.38673 - 2.84439i) q^{68} +(7.99725 + 8.39709i) q^{69} +(4.11152 + 2.00701i) q^{70} +(-3.43788 - 5.95458i) q^{71} +(-5.04582 + 3.83078i) q^{72} +(1.23957 + 0.715668i) q^{73} +(-1.34436 + 7.62423i) q^{74} +(8.56657 + 1.27037i) q^{75} +(1.91656 + 0.697573i) q^{76} +(-4.29586 + 0.757476i) q^{77} +(-0.934649 - 1.40661i) q^{78} +(-0.970806 - 0.814603i) q^{79} +(-7.64162 - 7.91838i) q^{80} +(-6.29826 - 6.42899i) q^{81} -9.53928i q^{82} +(-0.982501 + 1.17090i) q^{83} +(1.28774 - 0.855668i) q^{84} +(-9.33432 - 6.78651i) q^{85} +(-3.35061 - 1.21952i) q^{86} +(1.81742 - 16.2100i) q^{87} +(7.31144 + 1.28920i) q^{88} +(6.52774 - 11.3064i) q^{89} +(6.93367 - 8.61967i) q^{90} +(-0.366811 - 0.635335i) q^{91} +(1.64736 + 4.52610i) q^{92} +(1.42126 - 1.35358i) q^{93} +(-7.87952 + 6.61170i) q^{94} +(6.30422 + 0.664715i) q^{95} +(-6.55214 + 1.58548i) q^{96} +(4.74011 + 13.0234i) q^{97} +(-7.79835 + 4.50238i) q^{98} +(-0.514163 + 10.5345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.06000	−	1.26326i	0.749535	−	0.893261i	−0.247604	−	0.968861i	$-0.579643\pi$
$2$	1.06000	−	1.26326i	0.749535	−	0.893261i	0.997138	+	0.0756008i	$0.0240875\pi$
$3$	−0.958575	−	1.44261i	−0.553433	−	0.832893i
$3$	−0.958575	−	1.44261i	−0.553433	−	0.832893i
$4$	−0.124928	−	0.708504i	−0.0624641	−	0.354252i
$5$	−0.908813	−	2.04305i	−0.406434	−	0.913680i
$5$	−0.908813	−	2.04305i	−0.406434	−	0.913680i
$6$	−2.83849	−	0.318243i	−1.15881	−	0.129922i
$7$	−1.22191	−	0.215456i	−0.461840	−	0.0814348i	−0.0621128	−	0.998069i	$-0.519784\pi$
$7$	−1.22191	−	0.215456i	−0.461840	−	0.0814348i	−0.399727	+	0.916634i	$0.630895\pi$
$8$	1.82882	+	1.05587i	0.646587	+	0.373307i
$9$	−1.16227	+	2.76571i	−0.387423	+	0.921902i
$10$	−3.54425	−	1.01757i	−1.12079	−	0.321784i
$11$	3.30366	−	1.20243i	0.996092	−	0.362548i	0.208016	−	0.978125i	$-0.433299\pi$
$11$	3.30366	−	1.20243i	0.996092	−	0.362548i	0.788076	+	0.615578i	$0.211077\pi$
$12$	−0.902344	+	0.859377i	−0.260484	+	0.248081i
$13$	0.380059	+	0.452936i	0.105409	+	0.125622i	0.816170	−	0.577812i	$-0.196093\pi$
$13$	0.380059	+	0.452936i	0.105409	+	0.125622i	−0.710760	+	0.703434i	$0.751649\pi$
$14$	−1.56741	+	1.31521i	−0.418907	+	0.351505i
$15$	−2.07617	+	3.26948i	−0.536065	+	0.844177i
$16$	4.62449	−	1.68318i	1.15612	−	0.420794i
$17$	4.46967	−	2.58056i	1.08405	−	0.625879i	0.152067	−	0.988370i	$-0.451407\pi$
$17$	4.46967	−	2.58056i	1.08405	−	0.625879i	0.931987	+	0.362491i	$0.118074\pi$
$18$	2.26180	+	4.39990i	0.533112	+	1.03707i
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	−0.981551	−	0.191199i	$-0.938762\pi$
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	0.656359	+	0.754449i	$0.272096\pi$
$20$	−1.33397	+	0.899132i	−0.298285	+	0.201052i
$21$	0.860474	+	1.96928i	0.187771	+	0.429732i
$22$	1.98290	−	5.44797i	0.422756	−	1.16151i
$23$	−6.59324	+	1.16257i	−1.37479	+	0.242412i	−0.811742	−	0.584016i	$-0.801481\pi$
$23$	−6.59324	+	1.16257i	−1.37479	+	0.242412i	−0.563043	+	0.826427i	$0.690370\pi$
$24$	−0.229849	−	3.65042i	−0.0469177	−	0.745139i
$25$	−3.34812	+	3.71350i	−0.669624	+	0.742701i
$26$	0.975040			0.191221
$27$	5.10397	−	0.974431i	0.982259	−	0.187529i
$28$			0.892646i			0.168694i
$29$	7.21421	+	6.05345i	1.33965	+	1.12410i	0.981717	+	0.190348i	$0.0609616\pi$
$29$	7.21421	+	6.05345i	1.33965	+	1.12410i	0.357929	+	0.933749i	$0.383483\pi$
$30$	1.92947	+	6.08840i	0.352271	+	1.11159i
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	0.997366	−	0.0725319i	$-0.0231079\pi$
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	−0.962025	+	0.272962i	$0.911997\pi$
$32$	1.33116	−	3.65733i	0.235318	−	0.646531i
$33$	−4.90146	−	3.61329i	−0.853234	−	0.628992i
$34$	1.47793	−	8.38176i	0.253463	−	1.43746i
$35$	0.670302	+	2.69224i	0.113302	+	0.455072i
$36$	2.10471	+	0.477957i	0.350785	+	0.0796595i
$37$	−4.06570	+	2.34734i	−0.668398	+	0.385900i	−0.795469	−	0.605994i	$-0.792776\pi$
$37$	−4.06570	+	2.34734i	−0.668398	+	0.385900i	0.127072	+	0.991894i	$0.459442\pi$
$38$	1.59896	+	4.39311i	0.259386	+	0.712657i
$39$	0.289098	−	0.982452i	0.0462927	−	0.157318i
$40$	0.495142	−	4.69597i	0.0782888	−	0.742498i
$41$	4.43129	−	3.71830i	0.692052	−	0.580700i	−0.227448	−	0.973790i	$-0.573038\pi$
$41$	4.43129	−	3.71830i	0.692052	−	0.580700i	0.919500	+	0.393090i	$0.128594\pi$
$42$	3.39982	+	1.00044i	0.524603	+	0.154371i
$43$	−0.739520	−	2.03181i	−0.112776	−	0.309849i	0.870446	−	0.492264i	$-0.163831\pi$
$43$	−0.739520	−	2.03181i	−0.112776	−	0.309849i	−0.983222	+	0.182415i	$0.941608\pi$
$44$	−1.26465	−	2.19044i	−0.190653	−	0.330221i
$45$	6.70677	−	0.138934i	0.999786	−	0.0207111i
$46$	−5.52022	+	9.56131i	−0.813913	+	1.40974i
$47$	−6.14268	−	1.08312i	−0.896002	−	0.157989i	−0.293361	−	0.956002i	$-0.594774\pi$
$47$	−6.14268	−	1.08312i	−0.896002	−	0.157989i	−0.602641	+	0.798012i	$0.705885\pi$
$48$	−6.86110	−	5.05791i	−0.990314	−	0.730046i
$49$	−5.13120	−	1.86760i	−0.733029	−	0.266801i
$50$	1.14211	+	8.16587i	0.161519	+	1.15483i
$51$	−8.00727	−	3.97434i	−1.12124	−	0.556519i
$52$	0.273427	−	0.325858i	0.0379175	−	0.0451883i
$53$			8.21098i			1.12787i	0.825821	+	0.563933i	$0.190712\pi$
$53$			8.21098i			1.12787i	−0.825821	+	0.563933i	$0.809288\pi$
$54$	4.17926	−	7.48054i	0.568725	−	1.01797i
$55$	−5.45905	−	5.65676i	−0.736098	−	0.762758i
$56$	−2.00717	−	1.68421i	−0.268219	−	0.225063i
$57$	4.90059	−	0.308566i	0.649099	−	0.0408706i
$58$	15.2942	−	2.69677i	2.00822	−	0.354104i
$59$	−12.6981	−	4.62173i	−1.65315	−	0.601698i	−0.663886	−	0.747833i	$-0.731094\pi$
$59$	−12.6981	−	4.62173i	−1.65315	−	0.601698i	−0.989265	+	0.146136i	$0.953316\pi$
$60$	2.57581	+	1.06252i	0.332536	+	0.137171i
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	0.758255	+	0.651958i	$0.226052\pi$
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	−0.935509	+	0.353302i	$0.885059\pi$
$62$	1.61831	+	0.934331i	0.205525	+	0.118660i
$63$	2.01608	−	3.12903i	0.254002	−	0.394221i
$64$	1.71215	+	2.96553i	0.214019	+	0.370691i
$65$	0.579970	−	1.18811i	0.0719364	−	0.147367i
$66$	−9.76008	+	2.36173i	−1.20138	+	0.290709i
$67$	2.83000	+	3.37266i	0.345739	+	0.412036i	0.910691	−	0.413088i	$-0.135550\pi$
$67$	2.83000	+	3.37266i	0.345739	+	0.412036i	−0.564952	+	0.825124i	$0.691105\pi$
$68$	−2.38673	−	2.84439i	−0.289433	−	0.344933i
$69$	7.99725	+	8.39709i	0.962755	+	1.01089i
$70$	4.11152	+	2.00701i	0.491421	+	0.239884i
$71$	−3.43788	−	5.95458i	−0.408001	−	0.706679i	0.586664	−	0.809830i	$-0.300441\pi$
$71$	−3.43788	−	5.95458i	−0.408001	−	0.706679i	−0.994666	+	0.103151i	$0.967107\pi$
$72$	−5.04582	+	3.83078i	−0.594655	+	0.451462i
$73$	1.23957	+	0.715668i	0.145081	+	0.0837626i	0.570783	−	0.821101i	$-0.306640\pi$
$73$	1.23957	+	0.715668i	0.145081	+	0.0837626i	−0.425702	+	0.904863i	$0.639973\pi$
$74$	−1.34436	+	7.62423i	−0.156278	+	0.886298i
$75$	8.56657	+	1.27037i	0.989183	+	0.146690i
$76$	1.91656	+	0.697573i	0.219845	+	0.0800171i
$77$	−4.29586	+	0.757476i	−0.489559	+	0.0863224i
$78$	−0.934649	−	1.40661i	−0.105828	−	0.159267i
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	0.586540	−	0.809920i	$-0.300490\pi$
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	−0.695764	+	0.718270i	$0.744934\pi$
$80$	−7.64162	−	7.91838i	−0.854359	−	0.885302i
$81$	−6.29826	−	6.42899i	−0.699807	−	0.714332i
$82$		−	9.53928i		−	1.05344i
$83$	−0.982501	+	1.17090i	−0.107844	+	0.128523i	−0.817266	−	0.576260i	$-0.804511\pi$
$83$	−0.982501	+	1.17090i	−0.107844	+	0.128523i	0.709423	+	0.704783i	$0.248956\pi$
$84$	1.28774	−	0.855668i	0.140504	−	0.0933610i
$85$	−9.33432	−	6.78651i	−1.01245	−	0.736101i
$86$	−3.35061	−	1.21952i	−0.361305	−	0.131504i
$87$	1.81742	−	16.2100i	0.194848	−	1.73789i
$88$	7.31144	+	1.28920i	0.779402	+	0.137430i
$89$	6.52774	−	11.3064i	0.691939	−	1.19847i	−0.279262	−	0.960215i	$-0.590090\pi$
$89$	6.52774	−	11.3064i	0.691939	−	1.19847i	0.971202	−	0.238259i	$-0.0765767\pi$
$90$	6.93367	−	8.61967i	0.730873	−	0.908593i
$91$	−0.366811	−	0.635335i	−0.0384522	−	0.0666012i
$92$	1.64736	+	4.52610i	0.171750	+	0.471878i
$93$	1.42126	−	1.35358i	0.147378	−	0.140360i
$94$	−7.87952	+	6.61170i	−0.812711	+	0.681945i
$95$	6.30422	+	0.664715i	0.646799	+	0.0681983i
$96$	−6.55214	+	1.58548i	−0.668724	+	0.161817i
$97$	4.74011	+	13.0234i	0.481286	+	1.32232i	0.908392	+	0.418120i	$0.137311\pi$
$97$	4.74011	+	13.0234i	0.481286	+	1.32232i	−0.427106	+	0.904202i	$0.640467\pi$
$98$	−7.79835	+	4.50238i	−0.787753	+	0.454809i
$99$	−0.514163	+	10.5345i	−0.0516753	+	1.05876i
$100$	3.04930	+	1.90823i	0.304930	+	0.190823i
$101$	2.04974	−	11.6247i	0.203957	−	1.15670i	−0.695115	−	0.718898i	$-0.744647\pi$
$101$	2.04974	−	11.6247i	0.203957	−	1.15670i	0.899072	−	0.437800i	$-0.144242\pi$
$102$	−13.5084	+	5.90246i	−1.33753	+	0.584431i
$103$	−0.837596	+	2.30128i	−0.0825308	+	0.226751i	−0.974093	−	0.226146i	$-0.927387\pi$
$103$	−0.837596	+	2.30128i	−0.0825308	+	0.226751i	0.891563	+	0.452897i	$0.149610\pi$
$104$	0.216818	+	1.22963i	0.0212607	+	0.120576i
$105$	3.24133	−	3.54770i	0.316321	−	0.346220i
$106$	10.3726	+	8.70366i	1.00748	+	0.845374i
$107$		−	6.83945i		−	0.661195i	−0.943772	−	0.330597i	$-0.892750\pi$
$107$		−	6.83945i		−	0.661195i	0.943772	−	0.330597i	$-0.107250\pi$
$108$	−1.32802	−	3.49445i	−0.127789	−	0.336253i
$109$	18.7944			1.80018			0.900088	−	0.435708i	$-0.143502\pi$
$109$	18.7944			1.80018			0.900088	+	0.435708i	$0.143502\pi$
$110$	−12.9326	+	0.900022i	−1.23307	+	0.0858137i
$111$	7.28358	+	3.61514i	0.691327	+	0.343134i
$112$	−6.01338	+	1.06032i	−0.568211	+	0.100191i
$113$	4.71959	−	12.9670i	0.443982	−	1.21983i	−0.492870	−	0.870103i	$-0.664052\pi$
$113$	4.71959	−	12.9670i	0.443982	−	1.21983i	0.936852	−	0.349727i	$-0.113726\pi$
$114$	4.80484	−	6.51781i	0.450014	−	0.610449i
$115$	8.36720	+	12.4138i	0.780246	+	1.15759i
$116$	3.38763	−	5.86754i	0.314533	−	0.544788i
$117$	−1.69442	+	0.524697i	−0.156649	+	0.0485083i
$118$	−19.2985	+	11.1420i	−1.77657	+	1.02570i
$119$	−6.01754	+	2.19021i	−0.551627	+	0.200776i
$120$	−7.24911	+	3.78714i	−0.661750	+	0.345717i
$121$	1.04185	−	0.874216i	0.0947136	−	0.0794742i
$122$	8.45081	+	10.0713i	0.765101	+	0.911811i
$123$	−9.61179	−	2.82838i	−0.866666	−	0.255026i
$124$	0.766069	−	0.278826i	0.0687950	−	0.0250393i
$125$	10.6297	+	3.46550i	0.950748	+	0.309964i
$126$	−1.81574	−	5.86362i	−0.161759	−	0.522372i
$127$	7.40277	+	4.27399i	0.656890	+	0.379255i	0.791091	−	0.611699i	$-0.209514\pi$
$127$	7.40277	+	4.27399i	0.656890	+	0.379255i	−0.134201	+	0.990954i	$0.542847\pi$
$128$	13.2270	+	2.33227i	1.16911	+	0.206146i
$129$	−2.22224	+	3.01449i	−0.195657	+	0.265411i
$130$	−0.886129	−	1.99206i	−0.0777187	−	0.174715i
$131$	1.68189	+	9.53845i	0.146947	+	0.833379i	0.965783	+	0.259351i	$0.0835087\pi$
$131$	1.68189	+	9.53845i	0.146947	+	0.833379i	−0.818836	+	0.574028i	$0.805380\pi$
$132$	−1.94770	+	3.92410i	−0.169525	+	0.341549i
$133$	2.26101	−	2.69457i	0.196055	−	0.233649i
$134$	7.26035			0.627198
$135$	−6.62936	−	9.54209i	−0.570565	−	0.821253i
$136$	10.8990			0.934580
$137$	−9.51323	+	11.3374i	−0.812770	+	0.968622i	−0.999906	−	0.0137123i	$-0.995635\pi$
$137$	−9.51323	+	11.3374i	−0.812770	+	0.968622i	0.187136	+	0.982334i	$0.440080\pi$
$138$	19.0848	−	1.20168i	1.62461	−	0.102294i
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	0.958034	−	0.286653i	$-0.0925428\pi$
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	−0.998299	+	0.0583011i	$0.981432\pi$
$140$	1.82372	−	0.811248i	0.154133	−	0.0685630i
$141$	4.32570	+	9.89977i	0.364289	+	0.833711i
$142$	−11.1664	−	1.96893i	−0.937060	−	0.165229i
$143$	1.80021	+	1.03935i	0.150541	+	0.0869151i
$144$	−0.719730	+	14.7463i	−0.0599775	+	1.22886i
$145$	5.81113	−	20.2405i	0.482588	−	1.68088i
$146$	2.21803	−	0.807296i	0.183565	−	0.0668123i
$147$	2.22441	+	9.19258i	0.183466	+	0.758191i
$148$	2.17102	+	2.58732i	0.178456	+	0.212676i
$149$	−14.9253	+	12.5238i	−1.22273	+	1.02599i	−0.224054	+	0.974577i	$0.571929\pi$
$149$	−14.9253	+	12.5238i	−1.22273	+	1.02599i	−0.998677	+	0.0514162i	$0.983626\pi$
$150$	10.6854	−	9.47522i	0.872459	−	0.773649i
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.808796	−	0.588089i	$-0.799880\pi$
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.241557	+	0.970387i	$0.577658\pi$
$152$	−5.18465	+	2.99336i	−0.420530	+	0.242793i
$153$	1.94213	+	15.3611i	0.157012	+	1.24187i
$154$	−3.59673	+	6.22972i	−0.289833	+	0.502005i
$155$	2.10110	−	1.41620i	0.168765	−	0.113752i
$156$	−0.732187	−	0.0820907i	−0.0586219	−	0.00657252i
$157$	−4.04287	+	11.1077i	−0.322656	+	0.886491i	0.667258	+	0.744826i	$0.267468\pi$
$157$	−4.04287	+	11.1077i	−0.322656	+	0.886491i	−0.989915	+	0.141665i	$0.954755\pi$
$158$	−2.05811	+	0.362901i	−0.163735	+	0.0288708i
$159$	11.8453	−	7.87084i	0.939392	−	0.624198i
$160$	−8.68189	+	0.604203i	−0.686364	+	0.0477664i
$161$	8.30684			0.654671
$162$	−14.7977	+	1.14161i	−1.16261	+	0.0896932i
$163$		−	13.4522i		−	1.05366i	−0.849972	−	0.526828i	$-0.823381\pi$
$163$		−	13.4522i		−	1.05366i	0.849972	−	0.526828i	$-0.176619\pi$
$164$	−3.18802	−	2.67507i	−0.248943	−	0.208888i
$165$	−2.92762	+	13.2977i	−0.227915	+	1.03523i
$166$	0.437699	+	2.48231i	0.0339720	+	0.192665i
$167$	−0.885201	+	2.43207i	−0.0684989	+	0.188199i	−0.969219	−	0.246201i	$-0.920818\pi$
$167$	−0.885201	+	2.43207i	−0.0684989	+	0.188199i	0.900720	+	0.434401i	$0.143040\pi$
$168$	−0.505650	+	4.51002i	−0.0390117	+	0.347955i
$169$	2.19672	−	12.4582i	0.168978	−	0.958324i
$170$	−18.4675	+	4.59797i	−1.41640	+	0.352648i
$171$	−5.14273	−	6.77388i	−0.393274	−	0.518011i
$172$	−1.34716	+	0.777784i	−0.102720	+	0.0593055i
$173$	−5.65820	−	15.5458i	−0.430185	−	1.18192i	−0.945699	−	0.325042i	$-0.894621\pi$
$173$	−5.65820	−	15.5458i	−0.430185	−	1.18192i	0.515515	−	0.856881i	$-0.327601\pi$
$174$	−18.5510	−	19.4785i	−1.40635	−	1.47666i
$175$	4.89120	−	3.81620i	0.369740	−	0.288478i
$176$	13.2539	−	11.1213i	0.999047	−	0.838300i
$177$	5.50470	+	22.7487i	0.413759	+	1.70990i
$178$	−7.36349	−	20.2310i	−0.551917	−	1.51638i
$179$	−0.606831	−	1.05106i	−0.0453567	−	0.0785601i	0.842456	−	0.538765i	$-0.181109\pi$
$179$	−0.606831	−	1.05106i	−0.0453567	−	0.0785601i	−0.887812	+	0.460205i	$0.847776\pi$
$180$	−0.936300	−	4.73441i	−0.0697877	−	0.352882i
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	−0.789405	−	0.613872i	$-0.789611\pi$
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	0.926332	+	0.376709i	$0.122944\pi$
$182$	−1.19141	−	0.210078i	−0.0883135	−	0.0155720i
$183$	12.6535	−	5.52893i	0.935373	−	0.408710i
$184$	−13.2854	−	4.83549i	−0.979413	−	0.356477i
$185$	8.49069	+	6.17315i	0.624248	+	0.453859i
$186$	−0.203391	−	3.23022i	−0.0149134	−	0.236851i
$187$	11.6633	−	13.8998i	0.852906	−	1.01645i
$188$			4.48743i			0.327279i
$189$	−6.44655	+	0.0909880i	−0.468917	+	0.00661840i
$190$	7.52219	−	7.25928i	0.545717	−	0.526643i
$191$	2.91058	+	2.44226i	0.210602	+	0.176716i	0.741987	−	0.670415i	$-0.233884\pi$
$191$	2.91058	+	2.44226i	0.210602	+	0.176716i	−0.531385	+	0.847131i	$0.678328\pi$
$192$	2.63689	−	5.31265i	0.190301	−	0.383407i
$193$	−8.95492	+	1.57899i	−0.644589	+	0.113658i	−0.486380	−	0.873747i	$-0.661683\pi$
$193$	−8.95492	+	1.57899i	−0.644589	+	0.113658i	−0.158209	+	0.987406i	$0.550572\pi$
$194$	21.4764	+	7.81678i	1.54192	+	0.561212i
$195$	−2.26993	+	0.302223i	−0.162553	+	0.0216427i
$196$	−0.682172	+	3.86879i	−0.0487266	+	0.276342i
$197$	−5.83859	−	3.37091i	−0.415982	−	0.240167i	0.277375	−	0.960762i	$-0.410536\pi$
$197$	−5.83859	−	3.37091i	−0.415982	−	0.240167i	−0.693357	+	0.720594i	$0.743869\pi$
$198$	12.7628	+	11.8161i	0.907015	+	0.839736i
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	0.614554	−	0.788875i	$-0.289336\pi$
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	−0.990463	+	0.137782i	$0.956003\pi$
$200$	−10.0441	+	3.25616i	−0.710225	+	0.230245i
$201$	2.15268	−	7.31553i	0.151838	−	0.515998i
$202$	−12.5123	−	14.9115i	−0.880360	−	1.04917i
$203$	−7.51089	−	8.95113i	−0.527161	−	0.628246i
$204$	−1.81550	+	6.16969i	−0.127110	+	0.431965i
$205$	−11.6239	−	5.67412i	−0.811847	−	0.396298i
$206$	2.01926	+	3.49746i	0.140688	+	0.243680i
$207$	4.44780	−	19.5862i	0.309144	−	1.36133i
$208$	2.51995	+	1.45489i	0.174727	+	0.100879i
$209$	−1.73072	+	9.81541i	−0.119717	+	0.678946i
$210$	−1.04586	−	7.85521i	−0.0721710	−	0.542061i
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.847454	−	0.530868i	$-0.178134\pi$
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.307952	+	0.951402i	$0.400356\pi$
$212$	5.81751	−	1.02578i	0.399548	−	0.0704511i
$213$	−5.29470	+	10.6674i	−0.362787	+	0.730921i
$214$	−8.64002	−	7.24983i	−0.590619	−	0.495588i
$215$	−3.47902	+	3.35742i	−0.237267	+	0.228974i
$216$	10.3631	+	3.60708i	0.705122	+	0.245430i
$217$		−	1.40598i		−	0.0954443i
$218$	19.9221	−	23.7422i	1.34929	−	1.60803i
$219$	−0.155791	−	2.47425i	−0.0105274	−	0.167194i
$220$	−3.32585	+	4.57445i	−0.224229	+	0.308409i
$221$	2.86757	+	1.04371i	0.192894	+	0.0702075i
$222$	12.2875	−	5.36900i	0.824682	−	0.360344i
$223$	−19.2137	−	3.38789i	−1.28664	−	0.226870i	−0.511844	−	0.859078i	$-0.671037\pi$
$223$	−19.2137	−	3.38789i	−1.28664	−	0.226870i	−0.774798	+	0.632209i	$0.782149\pi$
$224$	−2.41456	+	4.18213i	−0.161329	+	0.279431i
$225$	−6.37904	−	13.5760i	−0.425270	−	0.905067i
$226$	−11.3779	−	19.7071i	−0.756846	−	1.31090i
$227$	−1.25836	−	3.45732i	−0.0835203	−	0.229470i	0.890902	−	0.454196i	$-0.150073\pi$
$227$	−1.25836	−	3.45732i	−0.0835203	−	0.229470i	−0.974422	+	0.224726i	$0.927851\pi$
$228$	−0.830843	−	3.43354i	−0.0550239	−	0.227392i
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	−0.745943	−	0.666009i	$-0.768001\pi$
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	0.526360	+	0.850262i	$0.323557\pi$
$230$	24.5511	+	2.58866i	1.61885	+	0.170691i
$231$	5.21065	+	5.47117i	0.342835	+	0.359976i
$232$	6.80187	+	18.6880i	0.446564	+	1.22693i
$233$	6.83118	−	3.94398i	0.447525	−	0.258379i	−0.259259	−	0.965808i	$-0.583478\pi$
$233$	6.83118	−	3.94398i	0.447525	−	0.258379i	0.706784	+	0.707429i	$0.250145\pi$
$234$	−1.13326	+	2.69667i	−0.0740835	+	0.176287i
$235$	3.36968	+	13.5342i	0.219814	+	0.882872i
$236$	−1.68816	+	9.57403i	−0.109890	+	0.623216i
$237$	−0.244567	+	2.18136i	−0.0158864	+	0.141694i
$238$	−3.61180	+	9.92335i	−0.234119	+	0.643235i
$239$	−4.95815	−	28.1191i	−0.320716	−	1.81887i	−0.538210	−	0.842811i	$-0.680899\pi$
$239$	−4.95815	−	28.1191i	−0.320716	−	1.81887i	0.217493	−	0.976062i	$-0.430212\pi$
$240$	−4.09811	+	18.6143i	−0.264532	+	1.20155i
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	0.257485	−	0.966282i	$-0.417106\pi$
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	−0.906890	+	0.421367i	$0.861551\pi$
$242$		−	2.24280i		−	0.144173i
$243$	−3.23719	+	15.2486i	−0.207666	+	0.978200i
$244$	5.73565			0.367187
$245$	0.847690	+	12.1806i	0.0541569	+	0.778190i
$246$	−13.7615	+	9.14411i	−0.877401	+	0.583007i
$247$	−1.65075	+	0.291072i	−0.105035	+	0.0185205i
$248$	−0.818435	+	2.24863i	−0.0519707	+	0.142788i
$249$	2.63096	+	0.294975i	0.166730	+	0.0186933i
$250$	15.6453	−	9.75464i	0.989497	−	0.616938i
$251$	−13.5512	+	23.4713i	−0.855341	+	1.48149i	0.0209869	+	0.999780i	$0.493319\pi$
$251$	−13.5512	+	23.4713i	−0.855341	+	1.48149i	−0.876328	+	0.481715i	$0.840014\pi$
$252$	−2.46880	−	1.03749i	−0.155520	−	0.0653560i
$253$	−20.3839	+	11.7687i	−1.28153	+	0.739890i
$254$	13.2461	−	4.82119i	0.831135	−	0.302509i
$255$	−0.842675	+	19.9712i	−0.0527703	+	1.25064i
$256$	11.7205	−	9.83471i	0.732534	−	0.614669i
$257$	−1.21645	−	1.44970i	−0.0758798	−	0.0904300i	0.726769	−	0.686882i	$-0.241021\pi$
$257$	−1.21645	−	1.44970i	−0.0758798	−	0.0904300i	−0.802649	+	0.596452i	$0.796577\pi$
$258$	1.45251	+	6.00263i	0.0904292	+	0.373708i
$259$	5.47368	−	1.99226i	0.340118	−	0.123793i
$260$	−0.914238	−	0.262482i	−0.0566986	−	0.0162784i
$261$	−25.1269	+	12.9167i	−1.55532	+	0.799522i
$262$	13.8324	+	7.98612i	0.854566	+	0.493384i
$263$	20.7228	+	3.65398i	1.27782	+	0.225314i	0.771054	−	0.636770i	$-0.219730\pi$
$263$	20.7228	+	3.65398i	1.27782	+	0.225314i	0.506766	+	0.862084i	$0.330841\pi$
$264$	−5.14874	−	11.7834i	−0.316883	−	0.725217i
$265$	16.7755	−	7.46225i	1.03051	−	0.458402i
$266$	−1.00727	−	5.71250i	−0.0617596	−	0.350256i
$267$	−22.5681	+	1.42100i	−1.38114	+	0.0869638i
$268$	2.03599	−	2.42640i	0.124368	−	0.148216i
$269$	1.06528			0.0649512			0.0324756	−	0.999473i	$-0.489661\pi$
$269$	1.06528			0.0649512			0.0324756	+	0.999473i	$0.489661\pi$
$270$	−19.0813	−	1.74002i	−1.16125	−	0.105894i
$271$	−5.32687			−0.323585			−0.161792	−	0.986825i	$-0.551727\pi$
$271$	−5.32687			−0.323585			−0.161792	+	0.986825i	$0.551727\pi$
$272$	16.3264	−	19.4571i	0.989934	−	1.17976i
$273$	−0.564927	+	1.13818i	−0.0341909	+	0.0688859i
$274$	4.23809	+	24.0354i	0.256032	+	1.45203i
$275$	−6.59581	+	16.2941i	−0.397742	+	0.982569i
$276$	4.95029	−	6.71511i	0.297972	−	0.404202i
$277$	−16.9171	−	2.98294i	−1.01645	−	0.179228i	−0.359487	−	0.933150i	$-0.617048\pi$
$277$	−16.9171	−	2.98294i	−1.01645	−	0.179228i	−0.656963	+	0.753923i	$0.728159\pi$
$278$	−3.90419	−	2.25408i	−0.234158	−	0.135191i
$279$	−3.31508	−	0.752817i	−0.198468	−	0.0450700i
$280$	−1.61680	+	5.63139i	−0.0966221	+	0.336540i
$281$	−11.6900	+	4.25480i	−0.697365	+	0.253820i	−0.666286	−	0.745697i	$-0.732117\pi$
$281$	−11.6900	+	4.25480i	−0.697365	+	0.253820i	−0.0310798	+	0.999517i	$0.509895\pi$
$282$	17.0912	+	5.02929i	1.01777	+	0.299490i
$283$	13.3156	+	15.8689i	0.791528	+	0.943306i	0.999393	−	0.0348514i	$-0.0110958\pi$
$283$	13.3156	+	15.8689i	0.791528	+	0.943306i	−0.207865	+	0.978158i	$0.566651\pi$
$284$	−3.78936	+	3.17965i	−0.224857	+	0.188677i
$285$	−5.08414	−	9.73173i	−0.301158	−	0.576458i
$286$	3.22120	−	1.17242i	0.190474	−	0.0693268i
$287$	−6.21578	+	3.58868i	−0.366906	+	0.211833i
$288$	8.56794	+	7.93240i	0.504871	+	0.467421i
$289$	4.81863	−	8.34611i	0.283449	−	0.490948i
$290$	−19.4092	−	28.7959i	−1.13975	−	1.69095i
$291$	14.2439	−	19.3220i	0.834993	−	1.13268i
$292$	0.352196	−	0.967650i	0.0206107	−	0.0566274i
$293$	−6.16081	+	1.08632i	−0.359919	+	0.0634634i	−0.350684	−	0.936494i	$-0.614051\pi$
$293$	−6.16081	+	1.08632i	−0.359919	+	0.0634634i	−0.00923499	+	0.999957i	$0.502940\pi$
$294$	13.9705	+	6.93414i	0.814776	+	0.404407i
$295$	2.09776	+	30.1431i	0.122137	+	1.75500i
$296$	−9.91394			−0.576236
$297$	15.6901	−	9.35638i	0.910432	−	0.542912i
$298$			32.1299i			1.86123i
$299$	−3.03239	−	2.54448i	−0.175367	−	0.147151i
$300$	−0.170145	−	6.22815i	−0.00982332	−	0.359583i
$301$	0.465862	+	2.64203i	0.0268518	+	0.152284i
$302$	−7.74692	+	21.2845i	−0.445785	+	1.22478i
$303$	−18.7348	+	8.18613i	−1.07628	+	0.470281i
$304$	−2.42268	+	13.7397i	−0.138950	+	0.788025i
$305$	17.2988	−	4.30699i	0.990528	−	0.246617i
$306$	21.4637	+	13.8294i	1.22700	+	0.790573i
$307$	15.8040	−	9.12444i	0.901981	−	0.520759i	0.0241389	−	0.999709i	$-0.492316\pi$
$307$	15.8040	−	9.12444i	0.901981	−	0.520759i	0.877843	+	0.478949i	$0.158982\pi$
$308$	1.07335	+	2.94900i	0.0611597	+	0.168035i
$309$	4.12275	−	0.997617i	0.234535	−	0.0567525i
$310$	0.438146	−	4.15542i	0.0248850	−	0.236012i
$311$	−3.62362	+	3.04058i	−0.205477	+	0.172416i	−0.739719	−	0.672916i	$-0.765042\pi$
$311$	−3.62362	+	3.04058i	−0.205477	+	0.172416i	0.534242	+	0.845332i	$0.320597\pi$
$312$	1.56605	−	1.49148i	0.0886602	−	0.0844385i
$313$	−11.8489	−	32.5545i	−0.669737	−	1.84009i	−0.526026	−	0.850469i	$-0.676319\pi$
$313$	−11.8489	−	32.5545i	−0.669737	−	1.84009i	−0.143711	−	0.989620i	$-0.545904\pi$
$314$	9.74647	+	16.8814i	0.550025	+	0.952672i
$315$	−8.22501	−	1.27525i	−0.463427	−	0.0718521i
$316$	−0.455868	+	0.789587i	−0.0256446	+	0.0444177i
$317$	1.01556	+	0.179070i	0.0570395	+	0.0100576i	0.202095	−	0.979366i	$-0.435225\pi$
$317$	1.01556	+	0.179070i	0.0570395	+	0.0100576i	−0.145056	+	0.989424i	$0.546336\pi$
$318$	2.61309	−	23.3068i	0.146535	−	1.30698i
$319$	31.1122	+	11.3239i	1.74195	+	0.634018i
$320$	4.50270	−	6.19312i	0.251709	−	0.346206i
$321$	−9.86669	+	6.55613i	−0.550705	+	0.365927i
$322$	8.80527	−	10.4937i	0.490699	−	0.584792i
$323$			14.6316i			0.814124i
$324$	−3.76813	+	5.26550i	−0.209341	+	0.292528i
$325$	−2.95446	−	0.105135i	−0.163884	−	0.00583185i
$326$	−16.9936	−	14.2593i	−0.941189	−	0.789752i
$327$	−18.0158	−	27.1130i	−0.996278	−	1.49936i
$328$	12.0301	−	2.12123i	0.664251	−	0.117125i
$329$	7.27246	+	2.64696i	0.400943	+	0.145931i
$330$	13.6952	+	17.7940i	0.753897	+	0.979526i
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	−0.862344	−	0.506322i	$-0.831005\pi$
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	0.983511	−	0.180848i	$-0.0578842\pi$
$332$	0.952329	+	0.549827i	0.0522658	+	0.0301757i
$333$	−1.76660	−	13.9728i	−0.0968090	−	0.765703i
$334$	2.13403	+	3.69624i	0.116769	+	0.202249i
$335$	4.31857	−	8.84694i	0.235949	−	0.483360i
$336$	7.29390	+	7.65858i	0.397915	+	0.417810i
$337$	5.97195	+	7.11709i	0.325313	+	0.387693i	0.903769	−	0.428021i	$-0.140789\pi$
$337$	5.97195	+	7.11709i	0.325313	+	0.387693i	−0.578456	+	0.815714i	$0.696345\pi$
$338$	−13.4095	−	15.9808i	−0.729378	−	0.869239i
$339$	−23.2304	+	5.62126i	−1.26170	+	0.305305i
$340$	−3.64215	+	7.46123i	−0.197523	+	0.404642i
$341$	1.99192	+	3.45010i	0.107868	+	0.186833i
$342$	−14.0085	−	0.683719i	−0.757492	−	0.0369713i
$343$	13.3892	+	7.73027i	0.722950	+	0.417395i
$344$	0.792885	−	4.49667i	0.0427495	−	0.242444i
$345$	9.88769	−	23.9702i	0.532335	−	1.29051i
$346$	−25.6361	−	9.33077i	−1.37820	−	0.501625i
$347$	24.7495	−	4.36400i	1.32862	−	0.234272i	0.536120	−	0.844142i	$-0.319889\pi$
$347$	24.7495	−	4.36400i	1.32862	−	0.234272i	0.792502	+	0.609870i	$0.208778\pi$
$348$	−11.7119	+	0.737440i	−0.627823	+	0.0395310i
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	0.592361	−	0.805673i	$-0.298196\pi$
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	−0.690570	+	0.723265i	$0.742640\pi$
$350$	0.363825	−	10.2241i	0.0194473	−	0.546499i
$351$	2.38116	+	1.94143i	0.127097	+	0.103626i
$352$		−	13.6832i		−	0.729319i
$353$	8.23024	−	9.80842i	0.438051	−	0.522049i	−0.501176	−	0.865346i	$-0.667099\pi$
$353$	8.23024	−	9.80842i	0.438051	−	0.522049i	0.939227	+	0.343296i	$0.111543\pi$
$354$	34.5726	+	17.1598i	1.83751	+	0.912034i
$355$	−9.04113	+	12.4354i	−0.479853	+	0.660001i
$356$	−8.82611	−	3.21244i	−0.467783	−	0.170259i
$357$	8.92789	+	6.58151i	0.472514	+	0.348331i
$358$	−1.97101	−	0.347542i	−0.104171	−	0.0183682i
$359$	0.774475	−	1.34143i	0.0408753	−	0.0707980i	−0.844864	−	0.534981i	$-0.820319\pi$
$359$	0.774475	−	1.34143i	0.0408753	−	0.0707980i	0.885739	+	0.464183i	$0.153652\pi$
$360$	12.4122	+	6.82740i	0.654180	+	0.359836i
$361$	5.48150	+	9.49423i	0.288500	+	0.499696i
$362$	−2.07800	−	5.70927i	−0.109218	−	0.300073i
$363$	−2.25985	−	0.664986i	−0.118611	−	0.0349027i
$364$	−0.404312	+	0.339258i	−0.0211917	+	0.0177819i
$365$	0.335606	−	3.18292i	0.0175664	−	0.166602i
$366$	6.42824	−	21.8453i	0.336009	−	1.14187i
$367$	1.69337	+	4.65249i	0.0883931	+	0.242858i	0.976011	−	0.217723i	$-0.0698631\pi$
$367$	1.69337	+	4.65249i	0.0883931	+	0.242858i	−0.887617	+	0.460582i	$0.847641\pi$
$368$	−28.5336	+	16.4739i	−1.48742	+	0.858760i
$369$	5.13336	+	16.5773i	0.267232	+	0.862980i
$370$	16.7985	−	4.18241i	0.873310	−	0.217433i
$371$	1.76911	−	10.0331i	0.0918474	−	0.520893i
$372$	−1.13657	−	0.837866i	−0.0589285	−	0.0434413i
$373$	5.91918	−	16.2628i	0.306484	−	0.842057i	−0.686852	−	0.726798i	$-0.741008\pi$
$373$	5.91918	−	16.2628i	0.306484	−	0.842057i	0.993335	−	0.115260i	$-0.0367700\pi$
$374$	−5.19594	−	29.4676i	−0.268676	−	1.52374i
$375$	−5.18998	−	18.6565i	−0.268009	−	0.963416i
$376$	−10.0903	−	8.46673i	−0.520365	−	0.436638i
$377$			5.56825i			0.286779i
$378$	−6.71841	+	8.24012i	−0.345558	+	0.423826i
$379$	−8.91774			−0.458073			−0.229037	−	0.973418i	$-0.573558\pi$
$379$	−8.91774			−0.458073			−0.229037	+	0.973418i	$0.573558\pi$
$380$	−0.316622	−	4.54960i	−0.0162424	−	0.233390i
$381$	−0.930389	−	14.7763i	−0.0476653	−	0.757012i
$382$	6.17043	−	1.08801i	0.315707	−	0.0556676i
$383$	−8.44098	+	23.1914i	−0.431314	+	1.18502i	0.513693	+	0.857974i	$0.328277\pi$
$383$	−8.44098	+	23.1914i	−0.431314	+	1.18502i	−0.945007	+	0.327051i	$0.893945\pi$
$384$	−9.31447	−	21.3171i	−0.475327	−	1.08783i
$385$	5.45169	+	8.08826i	0.277844	+	0.412216i
$386$	−7.49755	+	12.9861i	−0.381615	+	0.660977i
$387$	6.47892	+	0.316220i	0.329342	+	0.0160744i
$388$	8.63492	−	4.98537i	0.438372	−	0.253094i
$389$	−6.71441	+	2.44385i	−0.340434	+	0.123908i	−0.506579	−	0.862193i	$-0.669090\pi$
$389$	−6.71441	+	2.44385i	−0.340434	+	0.123908i	0.166145	+	0.986101i	$0.446868\pi$
$390$	−2.02435	+	3.18788i	−0.102507	+	0.161424i
$391$	−26.4695	+	22.2106i	−1.33862	+	1.12324i
$392$	−7.41211	−	8.83341i	−0.374368	−	0.446155i
$393$	12.1481	−	11.5696i	0.612790	−	0.583611i
$394$	−10.4473	+	3.80249i	−0.526325	+	0.191567i
$395$	−0.781995	+	2.72373i	−0.0393464	+	0.137046i
$396$	7.52797	−	0.951772i	0.378295	−	0.0478284i
$397$	−3.87921	−	2.23966i	−0.194692	−	0.112405i	0.399485	−	0.916740i	$-0.369189\pi$
$397$	−3.87921	−	2.23966i	−0.194692	−	0.112405i	−0.594177	+	0.804334i	$0.702522\pi$
$398$	−17.2238	−	3.03702i	−0.863352	−	0.152232i
$399$	−6.05458	−	0.678822i	−0.303108	−	0.0339836i
$400$	−9.23286	+	22.8085i	−0.461643	+	1.14043i
$401$	0.799427	+	4.53377i	0.0399215	+	0.226406i	0.998241	−	0.0592942i	$-0.0188850\pi$
$401$	0.799427	+	4.53377i	0.0399215	+	0.226406i	−0.958319	+	0.285700i	$0.907774\pi$
$402$	−6.95959	−	10.4739i	−0.347113	−	0.522390i
$403$	−0.430668	+	0.513250i	−0.0214531	+	0.0255668i
$404$	−8.49220			−0.422503
$405$	−7.41081	+	18.7104i	−0.368246	+	0.929728i
$406$	−19.2692			−0.956313
$407$	−10.6092	+	12.6435i	−0.525878	+	0.626717i
$408$	−10.4475	−	15.7230i	−0.517228	−	0.778406i
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	−0.990908	−	0.134542i	$-0.957044\pi$
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	0.885133	−	0.465339i	$-0.154067\pi$
$410$	−19.4892	+	8.66942i	−0.962505	+	0.428152i
$411$	25.4747	+	2.85615i	1.25657	+	0.140883i
$412$	1.73510	+	0.305945i	0.0854823	+	0.0150728i
$413$	14.5202	+	8.38323i	0.714491	+	0.412512i
$414$	−20.0278	−	26.3801i	−0.984312	−	1.29651i
$415$	3.28512	+	0.943172i	0.161260	+	0.0462985i
$416$	2.16246	−	0.787071i	0.106023	−	0.0385893i
$417$	−3.42880	+	3.26553i	−0.167909	+	0.159914i
$418$	10.5649	+	12.5907i	0.516744	+	0.615832i
$419$	−12.8029	+	10.7429i	−0.625462	+	0.524825i	−0.899515	−	0.436890i	$-0.856080\pi$
$419$	−12.8029	+	10.7429i	−0.625462	+	0.524825i	0.274053	+	0.961715i	$0.411636\pi$
$420$	−2.91849	−	1.85328i	−0.142408	−	0.0904310i
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	−0.141338	−	0.989961i	$-0.545140\pi$
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	0.528064	+	0.849205i	$0.322918\pi$
$422$	25.5070	−	14.7265i	1.24166	−	0.716875i
$423$	10.1350	−	15.7300i	0.492783	−	0.764818i
$424$	−8.66975	+	15.0164i	−0.421040	+	0.729263i
$425$	−5.38204	+	25.2382i	−0.261068	+	1.22423i
$426$	7.86338	+	17.9961i	0.380982	+	0.871914i
$427$	3.38323	−	9.29536i	0.163726	−	0.449834i
$428$	−4.84578	+	0.854441i	−0.234229	+	0.0413010i
$429$	−0.226253	−	3.59331i	−0.0109236	−	0.173487i
$430$	0.553530	+	7.95378i	0.0266936	+	0.383565i
$431$	−11.6530			−0.561306			−0.280653	−	0.959809i	$-0.590551\pi$
$431$	−11.6530			−0.561306			−0.280653	+	0.959809i	$0.590551\pi$
$432$	21.9631	−	13.0971i	1.05670	−	0.630136i
$433$			10.8242i			0.520178i	0.965585	+	0.260089i	$0.0837519\pi$
$433$			10.8242i			0.520178i	−0.965585	+	0.260089i	$0.916248\pi$
$434$	−1.77612	−	1.49034i	−0.0852567	−	0.0715388i
$435$	−34.7696	+	11.0188i	−1.66707	+	0.528310i
$436$	−2.34795	−	13.3159i	−0.112446	−	0.637716i
$437$	6.49152	−	17.8353i	0.310531	−	0.853178i
$438$	−3.29076	−	2.42590i	−0.157239	−	0.115914i
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	0.615998	+	0.787748i	$0.288753\pi$
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	−0.848274	+	0.529557i	$0.822358\pi$
$440$	−4.01082	−	16.1093i	−0.191208	−	0.767980i
$441$	11.1291	−	12.0207i	0.529956	−	0.572416i
$442$	4.35811	−	2.51615i	0.207294	−	0.119681i
$443$	9.57265	+	26.3006i	0.454810	+	1.24958i	0.929302	+	0.369321i	$0.120410\pi$
$443$	9.57265	+	26.3006i	0.454810	+	1.24958i	−0.474491	+	0.880260i	$0.657368\pi$
$444$	1.65142	−	5.61208i	0.0783728	−	0.266337i
$445$	−29.0320	−	3.06113i	−1.37625	−	0.145111i
$446$	−24.6463	+	20.6807i	−1.16704	+	0.979260i
$447$	32.3741	+	9.52645i	1.53124	+	0.450586i
$448$	−1.45315	−	3.99251i	−0.0686551	−	0.188628i
$449$	−12.5470	−	21.7321i	−0.592130	−	1.02560i	−0.993945	−	0.109878i	$-0.964954\pi$
$449$	−12.5470	−	21.7321i	−0.592130	−	1.02560i	0.401815	−	0.915721i	$-0.368379\pi$
$450$	−23.9118	−	6.33219i	−1.12721	−	0.298502i
$451$	10.1685	−	17.6123i	0.478815	−	0.829333i
$452$	−9.77675	−	1.72391i	−0.459860	−	0.0810857i
$453$	19.1493	+	14.1166i	0.899714	+	0.663256i
$454$	−5.70136	−	2.07512i	−0.267578	−	0.0973904i
$455$	−0.964659	+	1.32681i	−0.0452239	+	0.0622020i
$456$	9.28813	+	4.61009i	0.434956	+	0.215887i
$457$	10.7750	−	12.8412i	0.504036	−	0.600686i	−0.452694	−	0.891666i	$-0.649537\pi$
$457$	10.7750	−	12.8412i	0.504036	−	0.600686i	0.956729	+	0.290980i	$0.0939813\pi$
$458$			7.15325i			0.334249i
$459$	20.2985	−	17.5265i	0.947451	−	0.818067i
$460$	7.74990	−	7.47903i	0.361341	−	0.348711i
$461$	19.8382	+	16.6462i	0.923956	+	0.775291i	0.974722	−	0.223419i	$-0.0717219\pi$
$461$	19.8382	+	16.6462i	0.923956	+	0.775291i	−0.0507663	+	0.998711i	$0.516166\pi$
$462$	12.4348	−	0.782959i	0.578520	−	0.0364265i
$463$	17.0551	−	3.00727i	0.792616	−	0.139760i	0.237341	−	0.971426i	$-0.423724\pi$
$463$	17.0551	−	3.00727i	0.792616	−	0.139760i	0.555275	+	0.831667i	$0.312613\pi$
$464$	43.5511	+	15.8513i	2.02181	+	0.735878i
$465$	−4.05709	−	1.67355i	−0.188143	−	0.0776090i
$466$	2.25878	−	12.8102i	0.104636	−	0.593420i
$467$	−10.7327	−	6.19652i	−0.496649	−	0.286741i	0.230679	−	0.973030i	$-0.425905\pi$
$467$	−10.7327	−	6.19652i	−0.496649	−	0.286741i	−0.727329	+	0.686289i	$0.759238\pi$
$468$	0.583431	+	1.13495i	0.0269691	+	0.0524632i
$469$	−2.73135	−	4.73083i	−0.126122	−	0.218449i
$470$	20.6691	+	10.0895i	0.953393	+	0.465392i
$471$	19.8995	−	4.81526i	0.916921	−	0.221875i
$472$	−18.3426	−	21.8599i	−0.844288	−	1.00618i
$473$	−4.88625	−	5.82321i	−0.224670	−	0.267751i
$474$	2.49638	+	2.62119i	0.114663	+	0.120395i
$475$	−4.37131	−	13.4839i	−0.200569	−	0.618686i
$476$	2.30353	+	3.98983i	0.105582	+	0.182874i
$477$	−22.7092	−	9.54337i	−1.03978	−	0.436961i
$478$	−40.7774	−	23.5429i	−1.86512	−	1.07682i
$479$	3.96462	−	22.4845i	0.181148	−	1.02734i	−0.749657	−	0.661826i	$-0.769782\pi$
$479$	3.96462	−	22.4845i	0.181148	−	1.02734i	0.930805	−	0.365515i	$-0.119107\pi$
$480$	9.19388	+	11.9454i	0.419641	+	0.545233i
$481$	−2.60840	−	0.949380i	−0.118933	−	0.0432880i
$482$	−21.3728	+	3.76860i	−0.973503	+	0.171655i
$483$	−7.96273	−	11.9836i	−0.362317	−	0.545271i
$484$	−0.749542	−	0.628940i	−0.0340701	−	0.0285882i
$485$	22.2995	−	21.5201i	1.01257	−	0.977177i
$486$	15.8316	+	20.2530i	0.718134	+	0.918695i
$487$			3.22215i			0.146009i	0.997332	+	0.0730047i	$0.0232588\pi$
$487$			3.22215i			0.146009i	−0.997332	+	0.0730047i	$0.976741\pi$
$488$	−10.8218	+	12.8970i	−0.489881	+	0.583818i
$489$	−19.4063	+	12.8949i	−0.877583	+	0.583128i
$490$	16.2858	+	11.8406i	0.735719	+	0.534904i
$491$	24.5814	+	8.94691i	1.10934	+	0.403768i	0.830753	−	0.556641i	$-0.187910\pi$
$491$	24.5814	+	8.94691i	1.10934	+	0.403768i	0.278591	+	0.960410i	$0.410132\pi$
$492$	−0.803132	+	7.16333i	−0.0362080	+	0.322948i
$493$	47.8665	+	8.44015i	2.15580	+	0.380125i
$494$	−1.38210	+	2.39387i	−0.0621836	+	0.107705i
$495$	21.9898	−	8.52344i	0.988369	−	0.383100i
$496$	2.78830	+	4.82948i	0.125198	+	0.216850i
$497$	2.91784	+	8.01669i	0.130883	+	0.359598i
$498$	3.16145	−	3.01091i	0.141668	−	0.134922i
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.174745	−	0.984614i	$-0.444090\pi$
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.999999	−	0.00111367i	$-0.000354492\pi$
$500$	1.12737	−	7.96411i	0.0504174	−	0.356166i
$501$	4.35707	−	1.05432i	0.194660	−	0.0471034i
$502$	15.2861	+	41.9983i	0.682253	+	1.87447i
$503$	−13.7378	+	7.93150i	−0.612537	+	0.353648i	−0.773958	−	0.633237i	$-0.781726\pi$
$503$	−13.7378	+	7.93150i	−0.612537	+	0.353648i	0.161421	+	0.986886i	$0.448392\pi$
$504$	6.99091	−	3.59373i	0.311400	−	0.160077i
$505$	−25.6126	+	6.37692i	−1.13975	+	0.283769i
$506$	−6.74011	+	38.2250i	−0.299634	+	1.69931i
$507$	−20.0781	+	8.77311i	−0.891700	+	0.389628i
$508$	2.10332	−	5.77883i	0.0933198	−	0.256394i
$509$	−2.38054	−	13.5007i	−0.105516	−	0.598410i	−0.991013	−	0.133765i	$-0.957293\pi$
$509$	−2.38054	−	13.5007i	−0.105516	−	0.598410i	0.885497	−	0.464645i	$-0.153818\pi$
$510$	24.3356	+	22.2340i	1.07760	+	0.984539i
$511$	−1.36046	−	1.14156i	−0.0601830	−	0.0504995i
$512$			1.63110i			0.0720849i
$513$	−4.84240	+	13.9122i	−0.213797	+	0.614240i
$514$	−3.12079			−0.137652
$515$	5.46284	−	0.380178i	0.240722	−	0.0167526i
$516$	2.41340	+	1.19787i	0.106244	+	0.0527333i
$517$	−21.5957	+	3.80791i	−0.949779	+	0.167472i
$518$	3.28537	−	9.02649i	0.144351	−	0.396601i
$519$	−17.0027	+	23.0644i	−0.746337	+	1.01241i
$520$	2.31516	−	1.56048i	0.101526	−	0.0684315i
$521$	13.9166	−	24.1042i	0.609697	−	1.05603i	−0.381593	−	0.924330i	$-0.624625\pi$
$521$	13.9166	−	24.1042i	0.609697	−	1.05603i	0.991290	−	0.131696i	$-0.0420422\pi$
$522$	−10.3174	+	45.4335i	−0.451583	+	1.98857i
$523$	7.94269	−	4.58572i	0.347310	−	0.200519i	−0.316190	−	0.948696i	$-0.602404\pi$
$523$	7.94269	−	4.58572i	0.347310	−	0.200519i	0.663500	+	0.748177i	$0.269070\pi$
$524$	6.54791	−	2.38325i	0.286047	−	0.104113i
$525$	−10.1939	−	3.39800i	−0.444898	−	0.148301i
$526$	26.5821	−	22.3050i	1.15903	−	0.972545i
$527$	3.75927	+	4.48012i	0.163756	+	0.195157i
$528$	−28.7486	−	8.45959i	−1.25112	−	0.368156i
$529$	20.5063	−	7.46369i	0.891579	−	0.324508i
$530$	8.35525	−	29.1018i	0.362929	−	1.26410i
$531$	27.5409	−	29.7475i	1.19518	−	1.29093i
$532$	−2.19158	−	1.26531i	−0.0950170	−	0.0548581i
$533$	3.36830	+	0.593923i	0.145897	+	0.0257257i
$534$	−22.1271	+	30.0156i	−0.957533	+	1.29890i
$535$	−13.9734	+	6.21578i	−0.604121	+	0.268732i
$536$	1.61447	+	9.15611i	0.0697345	+	0.395484i
$537$	−0.934584	+	1.88294i	−0.0403303	+	0.0812550i
$538$	1.12920	−	1.34572i	0.0486832	−	0.0580183i
$539$	−19.1974			−0.826892
$540$	−5.93241	+	5.88901i	−0.255290	+	0.253422i
$541$	25.6800			1.10407			0.552035	−	0.833821i	$-0.313852\pi$
$541$	25.6800			1.10407			0.552035	+	0.833821i	$0.313852\pi$
$542$	−5.64650	+	6.72923i	−0.242538	+	0.289045i
$543$	−6.36879	+	0.401012i	−0.273311	+	0.0172091i
$544$	−3.48814	−	19.7822i	−0.149553	−	0.848155i
$545$	−17.0806	−	38.3979i	−0.731652	−	1.64479i
$546$	0.838997	+	1.92013i	0.0359058	+	0.0821738i
$547$	−38.7852	−	6.83888i	−1.65834	−	0.292409i	−0.735477	−	0.677549i	$-0.763042\pi$
$547$	−38.7852	−	6.83888i	−1.65834	−	0.292409i	−0.922858	+	0.385140i	$0.874153\pi$
$548$	9.22108	+	5.32379i	0.393905	+	0.227421i
$549$	−20.1054	−	12.9542i	−0.858079	−	0.552872i
$550$	13.5921	+	25.6040i	0.579568	+	1.09176i
$551$	−25.0881	+	9.13133i	−1.06879	+	0.389008i
$552$	5.75930	+	23.8009i	0.245132	+	1.01303i
$553$	1.01073	+	1.20454i	0.0429806	+	0.0512222i
$554$	−21.7004	+	18.2088i	−0.921962	+	0.773618i
$555$	0.766514	−	18.1662i	0.0325367	−	0.771113i
$556$	−1.84815	+	0.672672i	−0.0783790	+	0.0285276i
$557$	−3.57754	+	2.06550i	−0.151585	+	0.0875178i	−0.573874	−	0.818944i	$-0.694560\pi$
$557$	−3.57754	+	2.06550i	−0.151585	+	0.0875178i	0.422289	+	0.906461i	$0.361227\pi$
$558$	−4.46499	+	3.38982i	−0.189018	+	0.143503i
$559$	0.639222	−	1.10716i	0.0270362	−	0.0468281i
$560$	7.63132	+	11.3220i	0.322482	+	0.478442i
$561$	−31.2322	−	3.50167i	−1.31862	−	0.147840i
$562$	−7.01647	+	19.2776i	−0.295972	+	0.813176i
$563$	17.1381	−	3.02191i	0.722286	−	0.127358i	0.199592	−	0.979879i	$-0.436038\pi$
$563$	17.1381	−	3.02191i	0.722286	−	0.127358i	0.522694	+	0.852521i	$0.324927\pi$
$564$	6.47362	−	4.30153i	0.272589	−	0.181127i
$565$	−30.7814	+	2.14218i	−1.29498	+	0.0901223i
$566$	34.1610			1.43590
$567$	6.31076	+	9.21266i	0.265027	+	0.386895i
$568$		−	14.5199i		−	0.609239i
$569$	−3.52883	−	2.96104i	−0.147936	−	0.124133i	0.565816	−	0.824532i	$-0.308561\pi$
$569$	−3.52883	−	2.96104i	−0.147936	−	0.124133i	−0.713752	+	0.700398i	$0.753006\pi$
$570$	−17.6829	−	3.89306i	−0.740656	−	0.163062i
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	−0.985717	−	0.168407i	$-0.946138\pi$
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	0.868673	−	0.495386i	$-0.164974\pi$
$572$	0.511488	−	1.40530i	0.0213864	−	0.0587586i
$573$	0.733238	−	6.53993i	0.0306315	−	0.273209i
$574$	−2.05530	+	11.6562i	−0.0857864	+	0.486519i
$575$	17.7578	−	28.3764i	0.740549	−	1.18338i
$576$	−10.1918	+	1.28856i	−0.424656	+	0.0536899i
$577$	−23.9756	+	13.8423i	−0.998116	+	0.576262i	−0.907690	−	0.419641i	$-0.862156\pi$
$577$	−23.9756	+	13.8423i	−0.998116	+	0.576262i	−0.0904254	+	0.995903i	$0.528823\pi$
$578$	−5.43556	−	14.9341i	−0.226089	−	0.621176i
$579$	10.8618	+	11.4049i	0.451403	+	0.473972i
$580$	−15.0664	−	1.58860i	−0.625599	−	0.0659629i
$581$	1.45281	−	1.21905i	0.0602726	−	0.0505748i
$582$	−9.31017	−	38.4752i	−0.385919	−	1.59485i
$583$	9.87317	+	27.1263i	0.408905	+	1.12346i
$584$	1.51131	+	2.61766i	0.0625384	+	0.108320i
$585$	2.61189	+	2.98494i	0.107989	+	0.123412i
$586$	−5.15817	+	8.93422i	−0.213082	+	0.369069i
$587$	16.8114	+	2.96430i	0.693880	+	0.122350i	0.509455	−	0.860497i	$-0.329847\pi$
$587$	16.8114	+	2.96430i	0.693880	+	0.122350i	0.184424	+	0.982847i	$0.440958\pi$
$588$	6.23508	−	2.72441i	0.257130	−	0.112353i
$589$	−3.01873	−	1.09873i	−0.124385	−	0.0452723i
$590$	40.3023	+	29.3018i	1.65922	+	1.20633i
$591$	0.733801	+	11.6541i	0.0301845	+	0.479385i
$592$	−14.8508	+	17.6985i	−0.610366	+	0.727405i
$593$			7.85373i			0.322514i	0.986912	+	0.161257i	$0.0515548\pi$
$593$			7.85373i			0.322514i	−0.986912	+	0.161257i	$0.948445\pi$
$594$	4.81198	−	29.7385i	0.197438	−	1.22018i
$595$	9.94353	+	10.3037i	0.407645	+	0.422409i
$596$	10.7378	+	9.01007i	0.439837	+	0.369067i
$597$	−8.16694	+	16.4543i	−0.334251	+	0.673428i
$598$	−6.42867	+	1.13355i	−0.262888	+	0.0463543i
$599$	45.0491	+	16.3965i	1.84066	+	0.669944i	0.989404	+	0.145188i	$0.0463787\pi$
$599$	45.0491	+	16.3965i	1.84066	+	0.669944i	0.851253	+	0.524756i	$0.175843\pi$
$600$	14.3254	+	11.3685i	0.584832	+	0.464117i
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	−0.760999	−	0.648753i	$-0.775291\pi$
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	0.936992	−	0.349351i	$-0.113598\pi$
$602$	3.83139	+	2.21206i	0.156156	+	0.0901567i
$603$	−12.6170	+	3.90700i	−0.513804	+	0.159105i
$604$	4.94082	+	8.55775i	0.201039	+	0.348210i
$605$	−2.73291	−	1.33405i	−0.111109	−	0.0542370i
$606$	−9.51765	+	32.3442i	−0.386628	+	1.31389i
$607$	28.6468	+	34.1399i	1.16274	+	1.38570i	0.908148	+	0.418648i	$0.137496\pi$
$607$	28.6468	+	34.1399i	1.16274	+	1.38570i	0.254590	+	0.967049i	$0.418060\pi$
$608$	7.09240	+	8.45239i	0.287635	+	0.342790i
$609$	−5.71327	+	19.4156i	−0.231513	+	0.786761i
$610$	12.8959	−	26.4184i	0.522142	−	1.06965i
$611$	−1.84400	−	3.19389i	−0.0746001	−	0.129211i
$612$	10.6408	−	3.29504i	0.430128	−	0.133194i
$613$	5.10015	+	2.94457i	0.205993	+	0.118930i	0.599448	−	0.800414i	$-0.295387\pi$
$613$	5.10015	+	2.94457i	0.205993	+	0.118930i	−0.393455	+	0.919344i	$0.628720\pi$
$614$	5.22571	−	29.6365i	0.210893	−	1.19603i
$615$	2.95680	+	22.2078i	0.119229	+	0.895507i
$616$	−8.65617	−	3.15059i	−0.348767	−	0.126941i
$617$	30.2359	−	5.33141i	1.21725	−	0.214635i	0.472110	−	0.881539i	$-0.343492\pi$
$617$	30.2359	−	5.33141i	1.21725	−	0.214635i	0.745143	+	0.666905i	$0.232381\pi$
$618$	3.10987	−	6.26559i	0.125097	−	0.252039i
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.959219	+	0.282666i	$0.0912187\pi$
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.444938	+	0.895561i	$0.353226\pi$
$620$	−1.26587	−	1.31172i	−0.0508385	−	0.0526798i
$621$	−32.5188	+	12.3584i	−1.30494	+	0.495924i
$622$			7.80060i			0.312776i
$623$	−10.4124	+	12.4090i	−0.417162	+	0.497155i
$624$	−0.316711	−	5.02994i	−0.0126786	−	0.201359i
$625$	−2.58021	−	24.8665i	−0.103208	−	0.994660i
$626$	−53.6846	−	19.5396i	−2.14567	−	0.780960i
$627$	15.8189	−	6.91204i	0.631745	−	0.276040i
$628$	8.37491	+	1.47672i	0.334195	+	0.0589277i
$629$	−12.1149	+	20.9836i	−0.483053	+	0.836672i
$630$	−10.3295	+	9.03858i	−0.411537	+	0.360105i
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	0.698114	−	0.715987i	$-0.254023\pi$
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	−0.969120	+	0.246591i	$0.920690\pi$
$632$	−0.915317	−	2.51481i	−0.0364094	−	0.100034i
$633$	−7.27564	−	30.0673i	−0.289181	−	1.19507i
$634$	1.30271	−	1.09310i	0.0517371	−	0.0434126i
$635$	2.00425	−	19.0085i	0.0795362	−	0.754329i
$636$	−7.05633	−	7.40913i	−0.279802	−	0.293791i
$637$	−1.10425	−	3.03391i	−0.0437520	−	0.120208i
$638$	47.2841	−	27.2995i	1.87199	−	1.08080i
$639$	20.4644	−	2.58734i	0.809558	−	0.102354i
$640$	−7.25589	−	29.1430i	−0.286814	−	1.15198i
$641$	1.38566	−	7.85848i	0.0547304	−	0.310391i	−0.945137	−	0.326674i	$-0.894072\pi$
$641$	1.38566	−	7.85848i	0.0547304	−	0.310391i	0.999867	+	0.0162827i	$0.00518316\pi$
$642$	−2.17661	+	19.4137i	−0.0859039	+	0.766198i
$643$	5.16505	−	14.1909i	0.203690	−	0.559633i	−0.795220	−	0.606321i	$-0.792645\pi$
$643$	5.16505	−	14.1909i	0.203690	−	0.559633i	0.998909	+	0.0466885i	$0.0148668\pi$
$644$	−1.03776	−	5.88543i	−0.0408935	−	0.231918i
$645$	8.17835	+	1.80054i	0.322022	+	0.0708963i
$646$	18.4835	+	15.5095i	0.727225	+	0.610214i
$647$		−	44.8366i		−	1.76271i	−0.472455	−	0.881355i	$-0.656632\pi$
$647$		−	44.8366i		−	1.76271i	0.472455	−	0.881355i	$-0.343368\pi$
$648$	−4.73022	−	18.4077i	−0.185821	−	0.723121i
$649$	−47.5075			−1.86483
$650$	−3.26455	+	3.62081i	−0.128046	+	0.142020i
$651$	−2.02829	+	1.34774i	−0.0794950	+	0.0528221i
$652$	−9.53092	+	1.68056i	−0.373260	+	0.0658157i
$653$	6.37556	−	17.5167i	0.249495	−	0.685482i	−0.750210	−	0.661199i	$-0.770048\pi$
$653$	6.37556	−	17.5167i	0.249495	−	0.685482i	0.999705	−	0.0242823i	$-0.00773004\pi$
$654$	−53.3477	−	5.98119i	−2.08606	−	0.233883i
$655$	17.9590	−	12.1049i	0.701717	−	0.472976i
$656$	14.2339	−	24.6539i	0.555742	−	0.962573i
$657$	−3.42005	+	2.59650i	−0.133429	+	0.101299i
$658$	11.0526	−	6.38123i	0.430876	−	0.248766i
$659$	−8.86949	+	3.22823i	−0.345506	+	0.125754i	−0.508944	−	0.860800i	$-0.669964\pi$
$659$	−8.86949	+	3.22823i	−0.345506	+	0.125754i	0.163438	+	0.986554i	$0.447742\pi$
$660$	9.78723	+	0.412967i	0.380967	+	0.0160747i
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	−0.952610	−	0.304194i	$-0.901613\pi$
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	0.134153	+	0.990961i	$0.457169\pi$
$662$	−13.4565	−	16.0369i	−0.523003	−	0.623291i
$663$	−1.24311	−	5.13727i	−0.0482784	−	0.199515i
$664$	−3.03314	+	1.10397i	−0.117709	+	0.0428425i
$665$	−7.55999	−	2.17051i	−0.293164	−	0.0841686i
$666$	−19.5239	−	12.5795i	−0.756534	−	0.487446i
$667$	−54.6026	−	31.5248i	−2.11422	−	1.22065i
$668$	1.83372	+	0.323334i	0.0709486	+	0.0125102i
$669$	13.5303	+	30.9654i	0.523112	+	1.19719i
$670$	−6.59830	−	14.8333i	−0.254914	−	0.573059i
$671$	4.86712	+	27.6028i	0.187893	+	1.06559i
$672$	8.34774	−	0.525616i	0.322021	−	0.0202761i
$673$	−17.1645	+	20.4558i	−0.661642	+	0.788514i	−0.987620	−	0.156863i	$-0.949862\pi$
$673$	−17.1645	+	20.4558i	−0.661642	+	0.788514i	0.325979	+	0.945377i	$0.394306\pi$
$674$	15.3210			0.590144
$675$	−13.4701	+	22.2161i	−0.518466	+	0.855098i
$676$	−9.10112			−0.350043
$677$	−21.7428	+	25.9121i	−0.835645	+	0.995883i	0.164310	+	0.986409i	$0.447460\pi$
$677$	−21.7428	+	25.9121i	−0.835645	+	0.995883i	−0.999955	+	0.00947415i	$0.996984\pi$
$678$	−17.5232	+	35.3046i	−0.672973	+	1.35587i
$679$	−2.98604	−	16.9347i	−0.114594	−	0.649894i
$680$	−9.90514	−	22.2672i	−0.379845	−	0.853908i
$681$	−3.78134	+	5.12942i	−0.144901	+	0.196560i
$682$	6.46982	+	1.14080i	0.247742	+	0.0436836i
$683$	−15.0388	−	8.68268i	−0.575445	−	0.332233i	0.183876	−	0.982949i	$-0.441136\pi$
$683$	−15.0388	−	8.68268i	−0.575445	−	0.332233i	−0.759321	+	0.650716i	$0.774469\pi$
$684$	−4.15684	+	4.48989i	−0.158941	+	0.171675i
$685$	31.8087	+	9.13242i	1.21535	+	0.348932i
$686$	23.9579	−	8.71998i	0.914718	−	0.332930i
$687$	7.20762	+	2.12093i	0.274988	+	0.0809183i
$688$	−6.83981	−	8.15137i	−0.260765	−	0.310768i
$689$	−3.71905	+	3.12066i	−0.141685	+	0.118888i
$690$	−19.7996	−	37.8992i	−0.753759	−	1.44280i
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	−0.590553	−	0.806999i	$-0.701090\pi$
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	0.0663389	+	0.997797i	$0.478868\pi$
$692$	−10.3074	+	5.95096i	−0.391827	+	0.226222i
$693$	2.89799	−	12.7615i	0.110085	−	0.484768i
$694$	20.7216	−	35.8909i	0.786582	−	1.36240i
$695$	−5.06894	+	3.41660i	−0.192276	+	0.129599i
$696$	20.4394	−	27.7263i	0.774755	−	1.05096i
$697$	10.2111	−	28.0548i	0.386773	−	1.06265i
$698$	−3.88958	+	0.685839i	−0.147223	+	0.0259594i
$699$	−12.2378	−	6.07415i	−0.462877	−	0.229745i
$700$	−3.31484	−	2.98868i	−0.125289	−	0.112962i
$701$	−28.8893			−1.09113			−0.545567	−	0.838067i	$-0.683686\pi$
$701$	−28.8893			−1.09113			−0.545567	+	0.838067i	$0.683686\pi$
$702$	4.97657	−	0.950109i	0.187829	−	0.0358596i
$703$		−	13.3092i		−	0.501966i
$704$	9.22221	+	7.73836i	0.347575	+	0.291650i
$705$	16.2945	−	17.8347i	0.613686	−	0.671692i
$706$	−3.66652	−	20.7939i	−0.137991	−	0.782588i
$707$	−5.00922	+	13.7627i	−0.188391	+	0.517600i
$708$	15.4299	−	6.74206i	0.579889	−	0.253382i
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	−0.990829	−	0.135122i	$-0.956857\pi$
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	0.977289	+	0.211910i	$0.0679684\pi$
$710$	6.12550	+	24.6028i	0.229886	+	0.923328i
$711$	3.38129	−	1.73818i	0.126808	−	0.0651867i
$712$	23.8762	−	13.7849i	0.894798	−	0.516612i
$713$	−2.59472	−	7.12893i	−0.0971730	−	0.266981i
$714$	17.7777	−	4.30184i	0.665316	−	0.160992i
$715$	0.487396	−	4.62251i	0.0182276	−	0.172872i
$716$	−0.668871	+	0.561249i	−0.0249969	+	0.0209749i
$717$	−35.8122	+	34.1070i	−1.33743	+	1.27375i
$718$	−0.873632	−	2.40028i	−0.0326037	−	0.0895778i
$719$	9.24248	+	16.0084i	0.344686	+	0.597014i	0.985297	−	0.170852i	$-0.0546519\pi$
$719$	9.24248	+	16.0084i	0.344686	+	0.597014i	−0.640610	+	0.767866i	$0.721319\pi$
$720$	30.7815	−	11.9312i	1.14716	−	0.444649i
$721$	1.51929	−	2.63149i	0.0565814	−	0.0980019i
$722$	17.8041	+	3.13934i	0.662600	+	0.116834i
$723$	−2.53975	+	22.6526i	−0.0944542	+	0.842460i
$724$	−2.49076	−	0.906563i	−0.0925684	−	0.0336921i
$725$	−46.6335	+	6.52236i	−1.73193	+	0.242234i
$726$	−3.23549	+	2.14989i	−0.120080	+	0.0797899i
$727$	26.3979	−	31.4598i	0.979045	−	1.16678i	−0.00694522	−	0.999976i	$-0.502211\pi$
$727$	26.3979	−	31.4598i	0.979045	−	1.16678i	0.985990	−	0.166804i	$-0.0533448\pi$
$728$		−	1.54922i		−	0.0574179i
$729$	25.1010	−	9.94693i	0.929666	−	0.368405i
$730$	−3.66512	−	3.79786i	−0.135652	−	0.140565i
$731$	−8.54864	−	7.17316i	−0.316183	−	0.265309i
$732$	−5.49804	−	8.27432i	−0.203214	−	0.305828i
$733$	−3.29255	+	0.580566i	−0.121613	+	0.0214437i	−0.234123	−	0.972207i	$-0.575222\pi$
$733$	−3.29255	+	0.580566i	−0.121613	+	0.0214437i	0.112510	+	0.993651i	$0.464111\pi$
$734$	7.67229	+	2.79248i	0.283189	+	0.103072i
$735$	16.7593	−	12.8989i	0.618177	−	0.475784i
$736$	−4.52477	+	25.6612i	−0.166785	+	0.945886i
$737$	13.4048	+	7.73924i	0.493770	+	0.285078i
$738$	26.3829	+	11.0872i	0.971166	+	0.408126i
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	0.988423	−	0.151726i	$-0.0484830\pi$
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	−0.625610	+	0.780136i	$0.715150\pi$
$740$	3.31297	−	6.78689i	0.121787	−	0.249491i
$741$	2.00227	+	2.10238i	0.0735554	+	0.0772330i
$742$	−10.7992	−	12.8700i	−0.396450	−	0.472471i
$743$	−14.4345	−	17.2023i	−0.529549	−	0.631092i	0.433262	−	0.901268i	$-0.357362\pi$
$743$	−14.4345	−	17.2023i	−0.529549	−	0.631092i	−0.962811	+	0.270176i	$0.912918\pi$
$744$	4.02844	−	0.974796i	0.147690	−	0.0357378i
$745$	39.1512	+	19.1114i	1.43439	+	0.700187i
$746$	−14.2698	−	24.7161i	−0.522456	−	0.904921i
$747$	−2.09643	−	4.07821i	−0.0767045	−	0.149214i
$748$	−11.3051	−	6.52702i	−0.413357	−	0.238652i
$749$	−1.47360	+	8.35721i	−0.0538442	+	0.305366i
$750$	−29.0694	−	13.2196i	−1.06146	−	0.482712i
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.134177	−	0.990957i	$-0.542839\pi$
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.739761	+	0.672870i	$0.765061\pi$
$752$	−30.2299	+	5.33034i	−1.10237	+	0.194378i
$753$	46.8498	−	2.94990i	1.70730	−	0.107500i
$754$	7.03415	+	5.90235i	0.256169	+	0.214951i
$755$	21.3278	+	22.1002i	0.776197	+	0.804309i
$756$	0.869822	+	4.55604i	0.0316351	+	0.165701i
$757$			43.0981i			1.56643i	0.621753	+	0.783214i	$0.286421\pi$
$757$			43.0981i			1.56643i	−0.621753	+	0.783214i	$0.713579\pi$
$758$	−9.45282	+	11.2654i	−0.343342	+	0.409179i
$759$	36.5172	+	18.1250i	1.32549	+	0.657896i
$760$	10.8275	+	7.87210i	0.392753	+	0.285551i
$761$	−26.5013	−	9.64570i	−0.960673	−	0.349656i	−0.186376	−	0.982479i	$-0.559674\pi$
$761$	−26.5013	−	9.64570i	−0.960673	−	0.349656i	−0.774297	+	0.632822i	$0.781896\pi$
$762$	−19.6525	−	14.4876i	−0.711935	−	0.524829i
$763$	−22.9651	−	4.04937i	−0.831393	−	0.146597i
$764$	1.36674	−	2.36726i	0.0494469	−	0.0856445i
$765$	29.6185	−	17.9282i	1.07086	−	0.648197i
$766$	20.3493	+	35.2461i	0.735251	+	1.27349i
$767$	−2.73267	−	7.50796i	−0.0986711	−	0.271097i
$768$	−25.4227	−	7.48092i	−0.917363	−	0.269945i
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	−0.624831	−	0.780760i	$-0.714832\pi$
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	0.660398	+	0.750916i	$0.270388\pi$
$770$	15.9964	+	1.68665i	0.576470	+	0.0607828i
$771$	−0.925308	+	3.14451i	−0.0333241	+	0.113247i
$772$	2.23745	+	6.14733i	0.0805274	+	0.221247i
$773$	−4.24332	+	2.44988i	−0.152622	+	0.0881162i	−0.574366	−	0.818599i	$-0.694751\pi$
$773$	−4.24332	+	2.44988i	−0.152622	+	0.0881162i	0.421744	+	0.906715i	$0.361418\pi$
$774$	7.26714	−	7.84938i	0.261212	−	0.282140i
$775$	−4.80288	−	3.00561i	−0.172524	−	0.107965i
$776$	−5.08217	+	28.8224i	−0.182439	+	1.03466i
$777$	−8.12099	−	5.98668i	−0.291339	−	0.214771i
$778$	−4.03007	+	11.0725i	−0.144485	+	0.396970i
$779$	2.84770	+	16.1501i	0.102029	+	0.578637i
$780$	0.497705	+	1.57050i	0.0178207	+	0.0562329i
$781$	−18.5176	−	15.5381i	−0.662612	−	0.555997i
$782$			56.9812i			2.03764i
$783$	42.7198	+	23.8668i	1.52668	+	0.852931i
$784$	−26.8727			−0.959739
$785$	26.3678	−	1.83503i	0.941108	−	0.0654949i
$786$	−1.73847	−	27.6101i	−0.0620091	−	0.984818i
$787$	31.1341	−	5.48979i	1.10981	−	0.195690i	0.411448	−	0.911433i	$-0.365023\pi$
$787$	31.1341	−	5.48979i	1.10981	−	0.195690i	0.698363	+	0.715743i	$0.253912\pi$
$788$	−1.65890	+	4.55778i	−0.0590958	+	0.162364i
$789$	−14.5930	−	33.3975i	−0.519525	−	1.18898i
$790$	2.61186	+	3.87502i	0.0929260	+	0.137867i
$791$	−8.56074	+	14.8276i	−0.304385	+	0.527210i
$792$	−12.0634	+	18.7229i	−0.428655	+	0.665289i
$793$	−4.08231	+	2.35692i	−0.144967	+	0.0836967i
$794$	−6.94125	+	2.52641i	−0.246336	+	0.0896589i
$795$	−26.8457	−	17.0474i	−0.952118	−	0.604608i
$796$	−5.84498	+	4.90452i	−0.207170	+	0.173836i
$797$	16.6580	+	19.8522i	0.590057	+	0.703202i	0.975617	−	0.219480i	$-0.0704362\pi$
$797$	16.6580	+	19.8522i	0.590057	+	0.703202i	−0.385560	+	0.922683i	$0.625992\pi$
$798$	−7.27539	+	6.92896i	−0.257546	+	0.245283i
$799$	−30.2508	+	11.0104i	−1.07020	+	0.389520i
$800$	9.12464	+	17.1884i	0.322605	+	0.607703i
$801$	23.6831	+	31.1949i	0.836802	+	1.10222i
$802$	6.57473	+	3.79592i	0.232162	+	0.134039i
$803$	4.95568	+	0.873820i	0.174882	+	0.0308364i
$804$	−5.45201	−	0.611264i	−0.192278	−	0.0215576i
$805$	−7.54937	−	16.9713i	−0.266080	−	0.598160i
$806$	0.191860	+	1.08809i	0.00675797	+	0.0383264i
$807$	−1.02115	−	1.53679i	−0.0359461	−	0.0540974i
$808$	16.0228	−	19.0952i	0.563680	−	0.671768i
$809$	16.8506			0.592435			0.296217	−	0.955121i	$-0.404275\pi$
$809$	16.8506			0.592435			0.296217	+	0.955121i	$0.404275\pi$
$810$	15.7807	+	29.1949i	0.554476	+	1.02580i
$811$	−26.5505			−0.932313			−0.466156	−	0.884702i	$-0.654362\pi$
$811$	−26.5505			−0.932313			−0.466156	+	0.884702i	$0.654362\pi$
$812$	−5.40358	+	6.43974i	−0.189629	+	0.225991i
$813$	5.10621	+	7.68462i	0.179082	+	0.269511i
$814$	4.72633	+	26.8044i	0.165658	+	0.939493i
$815$	−27.4835	+	12.2255i	−0.962705	+	0.428241i
$816$	−43.7191	−	4.90166i	−1.53047	−	0.171592i
$817$	6.03666	+	1.06443i	0.211196	+	0.0372396i
$818$	−17.5932	−	10.1574i	−0.615132	−	0.355146i
$819$	2.18348	−	0.276061i	0.0762970	−	0.00964634i
$820$	−2.56798	+	8.94442i	−0.0896779	+	0.312353i
$821$	43.6959	−	15.9040i	1.52500	−	0.555054i	0.562608	−	0.826724i	$-0.309798\pi$
$821$	43.6959	−	15.9040i	1.52500	−	0.555054i	0.962390	+	0.271670i	$0.0875760\pi$
$822$	30.6113	−	29.1536i	1.06769	−	1.01685i
$823$	−0.257495	−	0.306870i	−0.00897570	−	0.0106968i	0.761538	−	0.648120i	$-0.224445\pi$
$823$	−0.257495	−	0.306870i	−0.00897570	−	0.0106968i	−0.770514	+	0.637424i	$0.780000\pi$
$824$	−3.96167	+	3.32424i	−0.138011	+	0.115805i
$825$	29.8286	−	6.10387i	1.03850	−	0.212509i
$826$	25.9816	−	9.45654i	0.904017	−	0.329035i
$827$	0.954191	−	0.550903i	0.0331805	−	0.0191568i	−0.483318	−	0.875445i	$-0.660569\pi$
$827$	0.954191	−	0.550903i	0.0331805	−	0.0191568i	0.516498	+	0.856288i	$0.327235\pi$
$828$	−14.4325	−	0.704416i	−0.501565	−	0.0244801i
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	−0.908086	−	0.418784i	$-0.862456\pi$
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	0.816721	+	0.577033i	$0.195790\pi$
$830$	4.67371	−	3.15020i	0.162227	−	0.109345i
$831$	11.9131	+	27.2642i	0.413260	+	0.945785i
$832$	−0.692479	+	1.90257i	−0.0240074	+	0.0659597i
$833$	−27.7542	+	4.89382i	−0.961627	+	0.169561i
$834$	0.490683	+	7.79295i	0.0169910	+	0.269848i
$835$	5.77333	−	0.401785i	0.199794	−	0.0139044i
$836$	7.17047			0.247996
$837$	2.09173	+	5.50401i	0.0723006	+	0.190246i
$838$			27.5609i			0.952075i
$839$	−27.5648	−	23.1296i	−0.951642	−	0.798523i	0.0279310	−	0.999610i	$-0.491108\pi$
$839$	−27.5648	−	23.1296i	−0.951642	−	0.798523i	−0.979573	+	0.201087i	$0.935553\pi$
$840$	9.67374	−	3.06569i	0.333776	−	0.105776i
$841$	10.3649	+	58.7823i	0.357410	+	2.02698i
$842$	4.76267	−	13.0853i	0.164132	−	0.450950i
$843$	17.3437	+	12.7856i	0.597350	+	0.440358i
$844$	2.23126	−	12.6541i	0.0768033	−	0.435573i
$845$	−27.4492	+	6.83418i	−0.944281	+	0.235103i
$846$	−9.12791	−	29.4770i	−0.313824	−	1.01344i
$847$	−1.46140	+	0.843742i	−0.0502145	+	0.0289913i
$848$	13.8205	+	37.9716i	0.474599	+	1.30395i
$849$	10.1287	−	34.4207i	0.347616	−	1.18132i
$850$	26.1774	+	33.5514i	0.897878	+	1.15080i
$851$	24.0772	−	20.2032i	0.825357	−	0.692557i
$852$	8.21938	+	2.41865i	0.281591	+	0.0828615i
$853$	−0.137118	−	0.376728i	−0.00469483	−	0.0128989i	0.937323	−	0.348462i	$-0.113296\pi$
$853$	−0.137118	−	0.376728i	−0.00469483	−	0.0128989i	−0.942018	+	0.335563i	$0.891074\pi$
$854$	−8.15623	−	14.1270i	−0.279101	−	0.483416i
$855$	−9.16560	+	16.6630i	−0.313457	+	0.569864i
$856$	7.22159	−	12.5082i	0.246829	−	0.427520i
$857$	−38.0088	−	6.70198i	−1.29836	−	0.228935i	−0.518599	−	0.855018i	$-0.673546\pi$
$857$	−38.0088	−	6.70198i	−1.29836	−	0.228935i	−0.779757	+	0.626083i	$0.784657\pi$
$858$	−4.77912	−	3.52310i	−0.163156	−	0.120277i
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	0.601202	−	0.799097i	$-0.294689\pi$
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	−0.0531029	+	0.998589i	$0.516911\pi$
$860$	2.81337	+	2.04546i	0.0959351	+	0.0697496i
$861$	11.1354	+	5.52695i	0.379493	+	0.188358i
$862$	−12.3522	+	14.7208i	−0.420719	+	0.501393i
$863$		−	23.2510i		−	0.791472i	−0.918364	−	0.395736i	$-0.870489\pi$
$863$		−	23.2510i		−	0.791472i	0.918364	−	0.395736i	$-0.129511\pi$
$864$	3.23038	−	19.9640i	0.109900	−	0.679190i
$865$	−26.6186	+	25.6882i	−0.905058	+	0.873425i
$866$	13.6738	+	11.4737i	0.464654	+	0.389891i
$867$	−16.6592	+	1.04895i	−0.565777	+	0.0356242i
$868$	−0.996144	+	0.175647i	−0.0338113	+	0.00596185i
$869$	−4.18672	−	1.52384i	−0.142025	−	0.0516928i
$870$	−22.9362	+	55.6030i	−0.777610	+	1.88512i
$871$	−0.452035	+	2.56362i	−0.0153166	+	0.0868648i
$872$	34.3716	+	19.8445i	1.16397	+	0.672019i
$873$	−41.5281	−	2.02688i	−1.40551	−	0.0685995i
$874$	−15.6496	−	27.1059i	−0.529356	−	0.916872i
$875$	−12.2419	−	6.52477i	−0.413851	−	0.220577i
$876$	−1.73355	+	0.419482i	−0.0585712	+	0.0141730i
$877$	−0.503887	−	0.600510i	−0.0170151	−	0.0202778i	0.757470	−	0.652870i	$-0.226435\pi$
$877$	−0.503887	−	0.600510i	−0.0170151	−	0.0202778i	−0.774485	+	0.632592i	$0.781991\pi$
$878$	29.7080	+	35.4047i	1.00260	+	1.19485i
$879$	7.47274	+	7.84636i	0.252049	+	0.264651i
$880$	−34.7667	−	16.9711i	−1.17198	−	0.572096i
$881$	4.60962	+	7.98410i	0.155302	+	0.268991i	0.933169	−	0.359438i	$-0.117032\pi$
$881$	4.60962	+	7.98410i	0.155302	+	0.268991i	−0.777867	+	0.628429i	$0.783698\pi$
$882$	−3.38848	−	26.8009i	−0.114096	−	0.902434i
$883$	31.4539	+	18.1599i	1.05851	+	0.611129i	0.925019	−	0.379921i	$-0.124049\pi$
$883$	31.4539	+	18.1599i	1.05851	+	0.611129i	0.133488	+	0.991050i	$0.457382\pi$
$884$	0.381232	−	2.16207i	0.0128222	−	0.0727183i
$885$	41.4741	−	31.9207i	1.39414	−	1.07300i
$886$	43.3716	+	15.7860i	1.45710	+	0.530340i
$887$	−33.0505	+	5.82770i	−1.10973	+	0.195675i	−0.698326	−	0.715779i	$-0.746072\pi$
$887$	−33.0505	+	5.82770i	−1.10973	+	0.195675i	−0.411401	+	0.911454i	$0.634960\pi$
$888$	9.50326	+	14.3020i	0.318908	+	0.479943i
$889$	−8.12468	−	6.81741i	−0.272493	−	0.228649i
$890$	−34.6410	+	33.4302i	−1.16117	+	1.12058i
$891$	−28.5378	−	13.6660i	−0.956051	−	0.457827i
$892$			14.0362i			0.469967i
$893$	11.3664	−	13.5459i	0.380361	−	0.453296i
$894$	46.3510	−	30.7989i	1.55021	−	1.03007i
$895$	−1.59588	+	2.19501i	−0.0533443	+	0.0733709i
$896$	−15.6597	−	5.69966i	−0.523154	−	0.190412i
$897$	−0.763925	+	6.81363i	−0.0255067	+	0.227501i
$898$	−40.7531	−	7.18587i	−1.35995	−	0.239796i
$899$	−5.33576	+	9.24181i	−0.177958	+	0.308232i
$900$	−8.82172	+	6.21560i	−0.294057	+	0.207187i
$901$	21.1890	+	36.7004i	0.705907	+	1.22267i
$902$	−11.4704	−	31.5146i	−0.381921	−	1.04932i
$903$	3.36487	−	3.20465i	0.111976	−	0.106644i
$904$	22.3228	−	18.7310i	0.742444	−	0.622985i
$905$	−8.19294	−	0.863861i	−0.272343	−	0.0287157i
$906$	38.1313	−	9.22696i	1.26683	−	0.306545i
$907$	−3.34276	−	9.18415i	−0.110994	−	0.304955i	0.871742	−	0.489965i	$-0.162990\pi$
$907$	−3.34276	−	9.18415i	−0.110994	−	0.304955i	−0.982737	+	0.185010i	$0.940768\pi$
$908$	−2.29232	+	1.32347i	−0.0760732	+	0.0439209i
$909$	29.7681	+	19.1800i	0.987345	+	0.636160i
$910$	0.653571	+	2.62504i	0.0216657	+	0.0870193i
$911$	6.63575	−	37.6332i	0.219852	−	1.24684i	−0.652433	−	0.757847i	$-0.726252\pi$
$911$	6.63575	−	37.6332i	0.219852	−	1.24684i	0.872285	−	0.488998i	$-0.162637\pi$
$912$	22.1434	−	9.67553i	0.733241	−	0.320389i
$913$	−1.83792	+	5.04965i	−0.0608264	+	0.167119i
$914$	−4.80022	−	27.2234i	−0.158777	−	0.900470i
$915$	−22.7955	−	20.8270i	−0.753597	−	0.688518i
$916$	2.39061	+	2.00596i	0.0789880	+	0.0662788i
$917$		−	12.0175i		−	0.396854i
$918$	−0.624136	−	44.2204i	−0.0205996	−	1.45949i
$919$	−15.3144			−0.505176			−0.252588	−	0.967574i	$-0.581282\pi$
$919$	−15.3144			−0.505176			−0.252588	+	0.967574i	$0.581282\pi$
$920$	2.19479	+	31.5373i	0.0723600	+	1.03975i
$921$	−28.3123	−	14.0526i	−0.932924	−	0.463049i
$922$	42.0570	−	7.41579i	1.38507	−	0.244226i
$923$	1.39045	−	3.82023i	0.0457673	−	0.125745i
$924$	3.22538	−	4.37527i	0.106107	−	0.143936i
$925$	4.89562	−	22.9572i	0.160967	−	0.754827i
$926$	14.2794	−	24.7327i	0.469252	−	0.812768i
$927$	−5.39114	−	4.99125i	−0.177068	−	0.163934i
$928$	31.7427	−	18.3267i	1.04201	−	0.601603i
$929$	0.281736	−	0.102544i	0.00924347	−	0.00336435i	−0.337394	−	0.941363i	$-0.609546\pi$
$929$	0.281736	−	0.102544i	0.00924347	−	0.00336435i	0.346638	+	0.937999i	$0.387323\pi$
$930$	−6.41466	+	3.35120i	−0.210345	+	0.109890i
$931$	11.8586	−	9.95056i	0.388651	−	0.326117i
$932$	−3.64773	−	4.34720i	−0.119485	−	0.142397i
$933$	7.85990	+	2.31286i	0.257321	+	0.0757198i
$934$	−19.2045	+	6.98986i	−0.628390	+	0.228715i
$935$	−38.9978	−	11.1964i	−1.27536	−	0.366163i
$936$	−3.65281	−	0.829512i	−0.119396	−	0.0271135i
$937$	13.1951	+	7.61820i	0.431065	+	0.248876i	0.699800	−	0.714338i	$-0.253272\pi$
$937$	13.1951	+	7.61820i	0.431065	+	0.248876i	−0.268735	+	0.963214i	$0.586606\pi$
$938$	−8.87151	−	1.56429i	−0.289665	−	0.0510758i
$939$	−35.6055	+	48.2992i	−1.16194	+	1.57619i
$940$	9.16804	−	4.07823i	0.299029	−	0.133017i
$941$	−1.63828	−	9.29115i	−0.0534064	−	0.302883i	0.946391	−	0.323024i	$-0.104699\pi$
$941$	−1.63828	−	9.29115i	−0.0534064	−	0.302883i	−0.999797	+	0.0201414i	$0.993588\pi$
$942$	15.0106	−	30.2425i	0.489072	−	0.985353i
$943$	−24.8938	+	29.6673i	−0.810654	+	0.966100i
$944$	−66.5014			−2.16444
$945$	6.04460	+	13.0879i	0.196631	+	0.425751i
$946$	−12.5357			−0.407570
$947$	36.2626	−	43.2160i	1.17837	−	1.40433i	0.282941	−	0.959137i	$-0.408690\pi$
$947$	36.2626	−	43.2160i	1.17837	−	1.40433i	0.895433	−	0.445195i	$-0.146866\pi$
$948$	1.57605	−	0.0992362i	0.0511878	−	0.00322304i
$949$	0.146959	+	0.833444i	0.00477048	+	0.0270547i
$950$	−21.6673	−	8.77090i	−0.702981	−	0.284566i
$951$	−0.715159	−	1.63671i	−0.0231906	−	0.0530740i
$952$	−13.3176	−	2.34825i	−0.431626	−	0.0761073i
$953$	13.0557	+	7.53769i	0.422915	+	0.244170i	0.696324	−	0.717728i	$-0.254818\pi$
$953$	13.0557	+	7.53769i	0.422915	+	0.244170i	−0.273409	+	0.961898i	$0.588151\pi$
$954$	−36.1275	+	18.5716i	−1.16967	+	0.601278i
$955$	2.34450	−	8.16602i	0.0758663	−	0.264246i
$956$	−19.3031	+	7.02574i	−0.624306	+	0.227229i
$957$	−13.4873	−	55.7377i	−0.435984	−	1.80174i
$958$	−24.2012	−	28.8419i	−0.781907	−	0.931840i
$959$	14.0671	−	11.8037i	0.454249	−	0.381160i
$960$	−13.2505	−	0.559096i	−0.427657	−	0.0180448i
$961$	27.9239	−	10.1635i	0.900770	−	0.327853i
$962$	−3.96422	+	2.28875i	−0.127812	+	0.0737921i
$963$	18.9159	+	7.94928i	0.609557	+	0.256162i
$964$	−4.73403	+	8.19958i	−0.152473	+	0.264091i
$965$	11.3643	+	16.8603i	0.365830	+	0.542754i
$966$	−23.5789	−	2.64360i	−0.758638	−	0.0850563i
$967$	3.00739	−	8.26273i	0.0967110	−	0.265711i	−0.881898	−	0.471440i	$-0.843734\pi$
$967$	3.00739	−	8.26273i	0.0967110	−	0.265711i	0.978609	+	0.205729i	$0.0659565\pi$
$968$	2.82842	−	0.498727i	0.0909089	−	0.0160297i
$969$	21.1077	−	14.0255i	0.678079	−	0.450563i
$970$	−3.54797	−	50.9815i	−0.113919	−	1.63692i
$971$	−1.79910			−0.0577358			−0.0288679	−	0.999583i	$-0.509190\pi$
$971$	−1.79910			−0.0577358			−0.0288679	+	0.999583i	$0.509190\pi$
$972$	11.2081	+	0.388579i	0.359501	+	0.0124637i
$973$			3.39195i			0.108741i
$974$	4.07041	+	3.41548i	0.130424	+	0.109439i
$975$	2.68040	+	4.36293i	0.0858416	+	0.139726i
$976$	6.81303	+	38.6386i	0.218080	+	1.23679i
$977$	4.35167	−	11.9561i	0.139222	−	0.382510i	−0.850413	−	0.526116i	$-0.823648\pi$
$977$	4.35167	−	11.9561i	0.139222	−	0.382510i	0.989635	+	0.143606i	$0.0458699\pi$
$978$	−4.28107	+	38.1839i	−0.136893	+	1.22099i
$979$	7.97027	−	45.2017i	0.254731	−	1.44465i
$980$	8.52410	−	2.12229i	0.272292	−	0.0677942i
$981$	−21.8441	+	51.9798i	−0.697430	+	1.65959i
$982$	37.3586	−	21.5690i	1.19216	−	0.688295i
$983$	−17.9343	−	49.2740i	−0.572015	−	1.57160i	−0.801315	−	0.598242i	$-0.795866\pi$
$983$	−17.9343	−	49.2740i	−0.572015	−	1.57160i	0.229301	−	0.973356i	$-0.426356\pi$
$984$	−14.5919	−	15.3214i	−0.465172	−	0.488429i
$985$	−1.58076	+	14.9921i	−0.0503672	+	0.477687i
$986$	61.4007	−	51.5213i	1.95540	−	1.64077i
$987$	−3.15266	−	13.0287i	−0.100350	−	0.414707i
$988$	0.412451	+	1.13320i	0.0131218	+	0.0360519i
$989$	7.23795	+	12.5365i	0.230154	+	0.398638i
$990$	12.5419	−	36.8138i	0.398609	−	1.17002i
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	−0.959593	−	0.281390i	$-0.909204\pi$
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	0.723488	+	0.690337i	$0.242538\pi$
$992$	4.34332	+	0.765844i	0.137900	+	0.0243156i
$993$	−20.1486	+	8.80392i	−0.639397	+	0.279384i
$994$	13.2201	+	4.81172i	0.419316	+	0.152618i
$995$	−13.9457	+	19.1812i	−0.442109	+	0.608086i
$996$	−0.119690	−	1.90089i	−0.00379252	−	0.0602321i
$997$	14.5685	−	17.3621i	0.461390	−	0.549864i	−0.484313	−	0.874895i	$-0.660930\pi$
$997$	14.5685	−	17.3621i	0.461390	−	0.549864i	0.945703	+	0.325031i	$0.105375\pi$
$998$		−	56.4909i		−	1.78819i
$999$	−18.4639	+	15.9425i	−0.584172	+	0.504397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.13	yes	96
3.2	odd	2		405.2.p.a.289.4		96
5.2	odd	4		675.2.l.h.151.13		96
5.3	odd	4		675.2.l.h.151.4		96
5.4	even	2	inner	135.2.p.a.124.4	yes	96
15.14	odd	2		405.2.p.a.289.13		96
27.5	odd	18		405.2.p.a.199.13		96
27.22	even	9	inner	135.2.p.a.49.4	✓	96
135.22	odd	36		675.2.l.h.76.13		96
135.49	even	18	inner	135.2.p.a.49.13	yes	96
135.59	odd	18		405.2.p.a.199.4		96
135.103	odd	36		675.2.l.h.76.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.4	✓	96	27.22	even	9	inner
135.2.p.a.49.13	yes	96	135.49	even	18	inner
135.2.p.a.124.4	yes	96	5.4	even	2	inner
135.2.p.a.124.13	yes	96	1.1	even	1	trivial
405.2.p.a.199.4		96	135.59	odd	18
405.2.p.a.199.13		96	27.5	odd	18
405.2.p.a.289.4		96	3.2	odd	2
405.2.p.a.289.13		96	15.14	odd	2
675.2.l.h.76.4		96	135.103	odd	36
675.2.l.h.76.13		96	135.22	odd	36
675.2.l.h.151.4		96	5.3	odd	4
675.2.l.h.151.13		96	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06000 - 1.26326i) q^{2} +(-0.958575 - 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-0.908813 - 2.04305i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(-1.22191 - 0.215456i) q^{7} +(1.82882 + 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +(-3.54425 - 1.01757i) q^{10} +(3.30366 - 1.20243i) q^{11} +(-0.902344 + 0.859377i) q^{12} +(0.380059 + 0.452936i) q^{13} +(-1.56741 + 1.31521i) q^{14} +(-2.07617 + 3.26948i) q^{15} +(4.62449 - 1.68318i) q^{16} +(4.46967 - 2.58056i) q^{17} +(2.26180 + 4.39990i) q^{18} +(-1.41748 + 2.45515i) q^{19} +(-1.33397 + 0.899132i) q^{20} +(0.860474 + 1.96928i) q^{21} +(1.98290 - 5.44797i) q^{22} +(-6.59324 + 1.16257i) q^{23} +(-0.229849 - 3.65042i) q^{24} +(-3.34812 + 3.71350i) q^{25} +0.975040 q^{26} +(5.10397 - 0.974431i) q^{27} +0.892646i q^{28} +(7.21421 + 6.05345i) q^{29} +(1.92947 + 6.08840i) q^{30} +(0.196771 + 1.11595i) q^{31} +(1.33116 - 3.65733i) q^{32} +(-4.90146 - 3.61329i) q^{33} +(1.47793 - 8.38176i) q^{34} +(0.670302 + 2.69224i) q^{35} +(2.10471 + 0.477957i) q^{36} +(-4.06570 + 2.34734i) q^{37} +(1.59896 + 4.39311i) q^{38} +(0.289098 - 0.982452i) q^{39} +(0.495142 - 4.69597i) q^{40} +(4.43129 - 3.71830i) q^{41} +(3.39982 + 1.00044i) q^{42} +(-0.739520 - 2.03181i) q^{43} +(-1.26465 - 2.19044i) q^{44} +(6.70677 - 0.138934i) q^{45} +(-5.52022 + 9.56131i) q^{46} +(-6.14268 - 1.08312i) q^{47} +(-6.86110 - 5.05791i) q^{48} +(-5.13120 - 1.86760i) q^{49} +(1.14211 + 8.16587i) q^{50} +(-8.00727 - 3.97434i) q^{51} +(0.273427 - 0.325858i) q^{52} +8.21098i q^{53} +(4.17926 - 7.48054i) q^{54} +(-5.45905 - 5.65676i) q^{55} +(-2.00717 - 1.68421i) q^{56} +(4.90059 - 0.308566i) q^{57} +(15.2942 - 2.69677i) q^{58} +(-12.6981 - 4.62173i) q^{59} +(2.57581 + 1.06252i) q^{60} +(-1.38440 + 7.85133i) q^{61} +(1.61831 + 0.934331i) q^{62} +(2.01608 - 3.12903i) q^{63} +(1.71215 + 2.96553i) q^{64} +(0.579970 - 1.18811i) q^{65} +(-9.76008 + 2.36173i) q^{66} +(2.83000 + 3.37266i) q^{67} +(-2.38673 - 2.84439i) q^{68} +(7.99725 + 8.39709i) q^{69} +(4.11152 + 2.00701i) q^{70} +(-3.43788 - 5.95458i) q^{71} +(-5.04582 + 3.83078i) q^{72} +(1.23957 + 0.715668i) q^{73} +(-1.34436 + 7.62423i) q^{74} +(8.56657 + 1.27037i) q^{75} +(1.91656 + 0.697573i) q^{76} +(-4.29586 + 0.757476i) q^{77} +(-0.934649 - 1.40661i) q^{78} +(-0.970806 - 0.814603i) q^{79} +(-7.64162 - 7.91838i) q^{80} +(-6.29826 - 6.42899i) q^{81} -9.53928i q^{82} +(-0.982501 + 1.17090i) q^{83} +(1.28774 - 0.855668i) q^{84} +(-9.33432 - 6.78651i) q^{85} +(-3.35061 - 1.21952i) q^{86} +(1.81742 - 16.2100i) q^{87} +(7.31144 + 1.28920i) q^{88} +(6.52774 - 11.3064i) q^{89} +(6.93367 - 8.61967i) q^{90} +(-0.366811 - 0.635335i) q^{91} +(1.64736 + 4.52610i) q^{92} +(1.42126 - 1.35358i) q^{93} +(-7.87952 + 6.61170i) q^{94} +(6.30422 + 0.664715i) q^{95} +(-6.55214 + 1.58548i) q^{96} +(4.74011 + 13.0234i) q^{97} +(-7.79835 + 4.50238i) q^{98} +(-0.514163 + 10.5345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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